What does it mean to magnify or glorify the Lord?

A magnifying glass allows us to see more details in an object, you can see the object on a more intimate level from a different perspective seeing details you wouldn't normally see without it. Maybe to magnify God means (of course many things not just this) to focus on God, stay tuned with Him so He can show us more of His amazing detail we wouldn't normally see when we don't focus our attention upon Him. God wants to show us many things and answer questions we have, but without our full attention (people often ask God but don't actually tune out other things in life and take time and listen to what He has to say and learn His voice) to magnify God could mean to focus on Him so He can show us more of Him that we have never experienced before because our attention is not fully of Him. (this is just my thought I could be wrong).

I think through our free will we have the ability to magnify the love of God to the world. Look at Mother Teresa such a small and diminutive woman; through her obedience to God she accomplished amazing things. This I believe is what we are all called to do; love God; but also to take his love and magnify it to the world. We are the lens that shines his love on the world. Without his faithful the world would be a very dark place.

I stumbled upon this question quite by accident this morning while reflecting on the word "magnifies" in the Magnificat (Luke 1:46-55). I wanted to offer my own take on the word. First, from childhood, I thought to magnify something means to make something appear bigger, period. However, used in the context of the Lord, that is impossible. So, it hit me all of a sudden, that to magnify something means to draw oneself closer to the true nature of the other. To our senses, we make something appear bigger when we magnify it. In reality, the object does not become bigger as we perceive. Rather, we are drawn intimately closer to the object's reality or true nature. Therefore, in the case of the Holy Mother, the Blessed Virgin Mary, I propose that to magnify means to be drawn closer to the true nature of the Lord, to His reality, His essence. To get to the true nature of the Lord, Jesus Christ, we have an opportunity to draw ourselves more closely to Jesus through the lens of Mary, mother of His humanity and divinity. This does not take anything away from our worship of the Lord, but rather intensifies our worship, drawing us intimately closer to the Lord.

St. Augustine says of the Blessed Virgin Mary (whose soul magnifies the Lord):

What the Lord magnified in her was, that she did the will of the Father, not that flesh gave birth to flesh. St. Augustine of Hippo - Tractate 10

That's what Mary magnified, as a handmaid, her soul magnifies the Lord. Augustine goes on to talk about:

May they ever say, “Exalted be the LORD who delights in the peace of his loyal servant.” (Psalm 35:27b NABRE)

which in his translation must have clicked with the Magnificat (Luke 1:46-55) because his says:

The Lord be magnified, they that wish the peace of His servant

So, exalting (or lifting the name of) God, it's an action of the soul, which we desire God to do to us. Mary's "Yes" meant something, it meant that she desired that her soul would be open to accept the Holy Spirit. While at the same time she, like John, must decrease as well as suffer, so her Son could increase.

Depending on your understanding or opinions regarding the faculties of the soul it would seem as though there's not a lot a person can do to influence one's soul. A devout prayer that God should allow a soul to magnify Him (and this is a prayer, in the Psalms and the Gospel) is the an excellent way, an perhaps one of the only ways, to open ourselves up to God's grace.

Sure, nothing we can do will make God more powerful or more holy than he already is, but we can acknowledge his greatness and make others aware of his greatness.

Like, suppose that a great orchestra is coming to town to give a concert. I tell a friend how great this orchestra is and encourage him to attend the show. Does me telling my friend this make the orchestra perform better? No. I'm just making my friend aware of how well they perform. Likewise, we can't make God greater, but we can tell others about his greatness.

In a different vein, suppose a man tells his wife how beautiful she is. Does his saying it make her more beautiful? No. (Well, it might, if it encourages her to put more effort into her hair styling or make-up or whatever. But let's assume she's already doing all she can.) But it pleases her to hear him say it. Likewise, our praise does not make God greater, but it pleases God to have us acknowledge him.

As John Piper says, we are to magnify God like a telescope, not a microscope! A microscope makes tiny things look bigger than they are, but a telescope helps us to see stupendously large things for what they really are.