What does "believe the Bible" mean?

I don't know that everyone who uses this phrase would say it quite this way, but the phrase could be reworded to make the meaning more plain.

"I believe the Bible is true."

How one applies this is not entirely uniform among the evangelicals that I know. It probably means that, in general, the speaker does not consider it proper to believe something appearing to be in opposition to a straightforward reading of the Bible.

If this is someone's response to something you have said, the more complete sentence might be, "I believe [God who wrote] the Bible, not you."

It may connote a "literal" reading of the text, but even that is a sliding scale. Even people who claim "literal readings" realize that some things are poetic, metaphorical, or figurative, though they probably restrict those allowances to certain places, like the books of wisdom or apocalyptic literature. Probably what most people mean when they speak of "literal" readings is that they prefer the simplest, most straightforward way of understanding what's written.'

It probably suggests that the speaker believes that the Bible is a sufficient and reliable source of information to lead us to Christ. I don't intend to prove such an assertion, but there are numerous evangelicals who claim to believe it.

Sometimes, when I hear people speak this way, it seems to me that they mean: "I believe what I read in the Bible, even if it doesn't make sense to me." Another phrase I've heard along these lines is "The Bible says it, and I believe it." It seems to me that this is a reactionary position to the theological acrobatics some "Bible experts" go through to read the scriptures and arrive at a conclusion that typical uneducated protestants don't consider reasonable. I don't subscribe to this philosophy, but I can at least understand why it might be appealing.

I frequently hear evangelicals refer to the Bible as if it were a person or living agent (e.g. "The Bible says, ..."). In a technical sense, this is not accurate, but if one believes that the Bible is the untainted, perfectly preserved Word of God, then it is only a matter of poetic usage to speak of the Bible as if it were a plenipotentiary representative of God himself.

It means to believe the propositions of Scripture to be true. Everyone believes some set of propositions to be true, which they cannot prove. For a Christian this axiom is: That the Bible is the Word of God (and hence is true in what it teaches).

Same applies to any belief....e.g. for a Muslim, they believe the propositions of the Koran to be true. Likewise Hindus believe the propositions of Vedas to be true. Atheists believe the propositions of Bertrand Russell, Dawkins and so on to be true. And if I believed all that your Pastor said (say his name is "Smith") then I would be called a Smithian in my belief.

But a Christian believes the propositions of the Bible to be true. For a person to say they are a Christian but say they don't believe the Biblical propositions is nonsense. A person may not state it exactly that way, but if they do not believe the Bible to be true then all they have left are their own muddled thoughts at least as far as being a Christian is concerned. So the propositions that God made the world, that Jesus is the Son of God, that He died and rose again from the grave and is coming back again, that God is a Trinity of persons etc all these propositions are clearly in the Bible (1 Cor.15:1-4). To believe these to be true is to be a Christian. Not to believe them is to be something else.

You ask, "Does it denote a literal interpretation"? It depends on the genre of the passage being read e.g. if the genre is metaphorical then the passage needs to be read metaphorically or else confusion will reign. Where it is historical genre, then it needs to be read as history, poetry as poetic and so on. The Bible is not written in a single genre.