What is a gospel, and how many gospels are there in the Catholic Bible?

The word "gospel" is a contraction of two Old English words gōd, meaning "good", and spel meaning "a story". Old English is a Germanic language, so both of these words are recognizable in the German "gut" and "Spiel" (although "spiel" means more like "play"). Spel may have boomeranged back into our language via Yiddish in the form of "spiel", in the expression "a good spiel" - which aptly describes (in American slang) what "Gospel" means.

In any case, our word "Gospel" corresponds directly to the Greek word εὐαγγέλιον - euangélion, alternately spelled evangelion. This word comes from the Greek adverb εὖ, meaning "well" combined with the word ἀγγελία, meaning "message" or "news". The latter is close to the word ἄγγελος - aggelos - which has an everyday meaning of "messenger", but also the special meaning of "angel" - a special kind of messenger.

The Greek word for Gospel appears 77 times in the New Testament, but it doesn't refer to the Gospel books, since these weren't written before the events they describe (make sense?). The word appears exactly once in the Greek Septuagint translation of the Old Testament, in a verse that describes someone who thought they were bringing good news, but weren't:

2 Kingdoms 4:10 LXX (2 Samuel)

ὅτι ὁ ἀπαγγείλας μοι ὅτι τέθνηκεν Σαουλ—καὶ αὐτὸς ἦν ὡς εὐαγγελιζόμενος ἐνώπιόν μου—καὶ κατέσχον αὐτὸν καὶ ἀπέκτεινα ἐν Σεκελακ, ὧ ἔδει με δοῦναι εὐαγγέλια

He that reported to me that Saul was dead, even he was as one bringing glad tidings before me: but I seized him and slew him in Ziklag, to whom I ought, as he thought, to have given a reward for his tidings.

The earliest mention of "Gospel" as one of the four canonical Gospels of the New Testament (Matthew, Mark, Luke, John) may have been by Papias of Hierapolis, who lived in the first century and died sometime after the year 100. A much later writer - Eusebius of Caesaria (263-339) - quotes a reference by Papias to a "Gospel" (euangélion) by Mark. The earliest original work we have, I think, that refers to Gospel books is by Justin Martyr (100-165), who writes in his First Apology:

So likewise have we been taught that the food which is blessed by the prayer of His word, and from which our blood and flesh by transmutation are nourished, is the flesh and blood of that Jesus who was made flesh. For the apostles, in the memoirs composed by them, which are called Gospels, have thus delivered unto us what was enjoined upon them; that Jesus took bread, and when He had given thanks, said, “This do ye in remembrance of Me, this is My body;” and that, after the same manner, having taken the cup and given thanks, He said, “This is My blood;” and gave it to them alone.

First Apology, Chapter LXVI, "Of the Eucharist"

It's not entirely clear, however, whether Justin is referring to the four canonical Gospels or - to the point of your question - the writings of the Apostles in general.

The first Church Father that I can identify who definitely spoke of the four Gospels in the same context we speak of them today was Irenaeus (130-202). Chapter XI of Book III of his collection Against Heresies is titled in part "The Gospels are four in number, neither four nor less" and mentions Matthew, Mark, Luke and John as the "Evangelists". Irenaeus makes some interesting comments about the distortion of Biblical texts even in his time, even to the point of excluding certain Gospels in order to reinforce heresy:

So firm is the ground upon which these Gospels rest, that the very heretics themselves bear witness to them, and, starting from these [documents], each one of them endeavours to establish his own peculiar doctrine. For the Ebionites, who use Matthew’s Gospel only, are confuted out of this very same, making false suppositions with regard to the Lord. But Marcion, mutilating that according to Luke, is proved to be a blasphemer of the only existing God, from those [passages] which he still retains. Those, again, who separate Jesus from Christ, alleging that Christ remained impassible, but that it was Jesus who suffered, preferring the Gospel by Mark, if they read it with a love of truth, may have their errors rectified. Those, moreover, who follow Valentinus, making copious use of that according to John, to illustrate their conjunctions, shall be proved to be totally in error by means of this very Gospel, as I have shown in the first book. Since, then, our opponents do bear testimony to us, and make use of these [documents], our proof derived from them is firm and true.

This answer is an excursus of sorts. I think the other answers may be somewhat more relevant to your question, but I think some extra information on etymology and what we know about the Gospels vis a vis the early Church is interesting.

How many gospels are there in the Roman Catholic Bible?

The quantity of gospels are the same in both the Catholic and Protestant Bibles. There are only four, in the same order, at the beginning of the New Testament.

Are there only gospels in the New Testament?

No, the New Testament contains other books, including:

• "Acts of the Apostles" (also known as "Acts," "Book of Acts"), which is a chronicle of the acts and ministry which the apostles and disciples of the Lord Jesus Christ performed after his resurrection and ascension. It is commonly attributed to the physician, Luke.

• twenty-one epistles (an epistle is a letter)

  1. thirteen epistles written by the apostle Paul

     • Epistle to the Romans (also known as "Romans")
     • First Epistle to the Corinthians (also known as "1 Corinthians")
     • Second Epistle to the Corinthians (also known as "2 Corinthians")
     • Epistle to the Galatians (also known as "Galatians")
     • Epistle to the Ephesians (also known as "Ephesians")
     • Epistle to the Philippians (also known as "Philippians")
     • Epistle to the Colossians (also known as "Colossians")
     • First Epistle to the Thessalonians (also known as "1 Thessalonians")
     • Second Epistle to the Thessalonians (also known as "2 Thessalonians")
     • First Epistle to Timothy (also known as "1 Timothy")
     • Second Epistle to Timothy (also known as "2 Timothy")
     • Epistle to Titus (also known as "Titus")
     • Epistle to Philemon (also known as "Philemon")

  2. one epistle written to the Jewish believers in the Lord Jesus Christ (i.e., the Hebrews), sometimes attributed to the apostle Paul, but whose author is otherwise considered to be unknown

     • Epistle to the Hebrews (also known as "Hebrews")

  3. one epistle written by James, the brother of the Lord Jesus Christ

     • Epistle of James (also known as "James")

  4. two epistles written by the apostle Peter

     • First Epistle of Peter (also known as "1 Peter")
     • Second Epistle of Peter (also known as "2 Peter")

  5. three epistles supposedly written by a John, perhaps the same author as the Gospel of John

     • First Epistle of John (also known as "1 John")
     • Second Epistle of John (also known as "2 John")
     • Third Epistle of John (also known as "3 John")

  6. one epistle written by Jude, another brother of the Lord Jesus Christ

     • Epistle of Jude (also known as "Jude")

• the Book of Revelation (formerly known as "the Apocalypse"; also known as "Revelation")

What are the names of gospels?

The names of the gospels in order are:

1. Gospel of Matthew (also known as "Matthew")
2. Gospel of Mark (also known as "Mark")
3. Gospel of Luke (also known as "Luke")
4. Gospel of John (also known as "John")

Is there a difference between books and gospels?

The smallest division of the Bible is a "verse." A collection of related verses (not necessarily composed by the same author) is a "book." The Protestant Bible contains 39 books in the Old Testament and 27 books in the New Testament. The Catholic Bible not only contains those books found in the Protestant Bible but additional books known as deuterocanonical books. (However, if you ask a Catholic, they would probably say that the Protestant Bible is missing these books.)

A gospel is a book of the Bible. It is simply a different genre of literature than the other books of the Bible (e.g., epistles).

I've read that there are 73 books in the Catholic Bible, but are all of these considered gospels? Or are there just 4 gospels in total, including: Matthew, Mark, Luke and John and no others between the Old and New Testament?

The latter. There are only four gospels in both Protestant and Catholic Bibles. There is absolutely no exception to this.