The concept of eating unclean meat (in particular that of pigs) is still being debated today.
Here's what the book of Leviticus says.
And the swine, though he divide the hoof, and be clovenfooted, yet he cheweth not the cud; he is unclean to you. Of their flesh shall ye not eat, and their carcase shall ye not touch; they are unclean to you.
- Leviticus 11:7-8 (KJV)
But then people say that we are no longer under the old covenant (which is true), and that this commandment is no longer valid.
God doesn't change however, and swine flesh is still considered unclean - even today.
For I am the Lord, I change not; therefore ye sons of Jacob are not consumed.
- Malachi 3:6 (KJV)
Swine wallow in their own filth, so it's not a big jump to call them unclean.
Some say that the whole idea of "unclean meat" was abolished in a vision to Peter.
On the morrow, as they went on their journey, and drew nigh unto the city, Peter went up upon the housetop to pray about the sixth hour: And he became very hungry, and would have eaten: but while they made ready, he fell into a trance, And saw heaven opened, and a certain vessel descending upon him, as it had been a great sheet knit at the four corners, and let down to the earth: Wherein were all manner of fourfooted beasts of the earth, and wild beasts, and creeping things, and fowls of the air. And there came a voice to him, Rise, Peter; kill, and eat. But Peter said, Not so, Lord; for I have never eaten any thing that is common or unclean. And the voice spake unto him again the second time, What God hath cleansed, that call not thou common. This was done thrice: and the vessel was received up again into heaven.
- Acts 10:9-16 (KJV)
However the vision here is a clear reference to the Gentiles being treated the same as the Jews.
While Peter yet spake these words, the Holy Ghost fell on all them which heard the word. And they of the circumcision which believed were astonished, as many as came with Peter, because that on the Gentiles also was poured out the gift of the Holy Ghost. For they heard them speak with tongues, and magnify God. Then answered Peter, Can any man forbid water, that these should not be baptized, which have received the Holy Ghost as well as we? And he commanded them to be baptized in the name of the Lord. Then prayed they him to tarry certain days.
- Acts 10:44-48 (KJV)
Jesus also placed a lot of emphasis on not so much what goes in the mouth, but what comes out of the mouth.
Not that which goeth into the mouth defileth a man; but that which cometh out of the mouth, this defileth a man.
- Matthew 15:11 (KJV)
So yeah, that's why we don't eat unclean meat (especially pigs).
Poor animals. Why not become vegetarian?