If you read through the Gospels you'll see where Jesus says multiple times in multiple ways, "For this reason I came ..." You can (and should) hunt those down to see what our Savior's intent was when He came to earth. Another explanation (not an alternate explanation; an additional one) is given in Titus.

[Christ] gave Himself for us to redeem us from all lawlessness and to purify for Himself a people for His own possession who are zealous for good works. (Titus 2:14)

That, as it turns out, is a pretty comprehensive (and surprising) answer.

We learn here that His giving of Himself was intentional -- with a purpose. That purpose was to redeem us. "Redeem" is literally "to ransom." Redemption is the act of buying something back or paying a price for something. We were in debt; He paid the price. So we read that our "certificate of debt" with its legal demands was canceled at the cross (Colossians 2:13-14). Paid in full.

Beyond redemption, He redeemed us with a purpose. He bought us out of lawlessness and bought us to "purify for Himself a people." Not just a debt paid, but a purification accomplished. That purification was for a purpose. It was "to purify for Himself a people for His own possession." Now that's a bit of a surprise. He didn't want friends, pals, "buds." He didn't simply want to set us free. He wanted a possession. He wanted to reassert His ownership.

What does that ownership look like? Those who are redeemed and, consequently, purified for His ownership are "zealous for good works." Now that is interesting. There are those who argue that works have nothing to do with it, and they don't ... as a cause; they do as an effect. If Christ's will -- His intent, His purpose, His aim -- is to be fulfilled in the people He redeemed, we will be zealous for good works. We won't be lackadaisical. We won't be careless. We will certainly trip up and fall short, but we will certainly aim for good works on an ongoing, ever-increasing way.

Jesus came for lots of reasons. He came to call sinners to repentance (Mark 2:17), to seek and to save the lost (Luke 19:10), to give Himself as a ransom for many (Matthew 20:28). He came to do the Father's will (John 6:38), to give us abundant life (John 10:10), and even for judgment (John 9:39). He came for lots of reasons. One of them is here. He redeemed us to purify us and make us His own possession, zealous for good works. I really want to do my part in His mission.