It is written by Paul and is considered one of the Pastoral Epistles. Did you know that there were different kinds of Epistles? Well there are...isn't learning fun :-) I have learned that there are missionary journey epistles, prison epistles, and pastoral epistles. Titus falls into the pastoral category because it is a letter Paul has written to Titus to help him oversee and grow the church. And that answers Why?
But who was Titus? He was a Gentile Christian (see Galatians 2:3) who ministered with Paul (see Galatians 2:1) and was left in Crete to continue to grow the church (see Titus 1:5).
What do we know about Crete at this time? Crete was deplorable, full of sin and depravity. The quote below is what someone from Crete says of his own people!
Titus 1:12 One of them, a prophet of their own, said, “Cretans are always liars, evil beasts, lazy gluttons.”
Where? There are two important locations we learn about in Titus. Titus is on the island of Crete and in Titus 3:12 Paul writes that he has decided to spend the winter at Nicopolis, so the assumption is that he was not there yet.
When? According to the Blue Letter Bible resource Titus was written late in Paul's ministry, in about 65 AD and was one of the last books he wrote.