Trees sometimes produce more fruit than they can bring to full-size, so you have to "thin" the fruit to get the fruit to reach full size. Thinning fruit simply means picking off some of the fruit on each branch early in the season, so the rest of the fruit can receive more resources from the tree and reach larger sizes.
Imagine this - if every six inches or so of a tree-branch can produce 1 large fruit, but four fruits are growing within that six inches of branch, then the nutrients the branch will provide will be divided between those four fruit and they'll be smaller.
There's a proper balance you want that'll vary from tree to tree, and sometimes trees will on their own "drop" half their crop early on, to thin themselves. Most of the time, you need to thin them. Trees don't always produce so much that they require thinning though - some years they'll produce the right amount on their own. Unfortunately, if they overproduce one year, and aren't thinned, they may produce too little the next year, or even produce nothing, to recover from the overproduction. So don't be shocked if you get zero mangoes next year - this is just because it overproduced this year, and wasn't thinned.
Here's more detailed information from USA's Oregon State University.
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