The authors of New Testament books were pretty skimpy with their titles. So skimpy, in fact, that they didn't give us any. But later generations of Christians, who liked fancy names, figure they should have something to help them tell which book was which. With 1 and 2 Corinthians, they took the simple route.
The most commonly used titles for these two—The First Epistle to the Corinthians and The Second Epistle to the Corinthians—pretty much say it all. It just means that these books of the Bible are:
that were sent to the Christian church in Corinth
and that one came first and one came second.
Sometimes you'll see alternate titles for these two like "The First Letter of St. Paul to the Corinthians" or even just "Second Corinthians." These all mean the same thing. Paul wrote 'em. The Corinthians read 'em. Then they ended up in the Bible. Ta-da!