Leviticus 11 begins a detailed section of very specific laws for the people of Israel.  This chapter deals with food, specifically which animals could be eaten and which could not. The overall emphasis is the issue of what is "clean" or "unclean".   The term unclean is the Hebrew word "tame" (pronounced, taw-may )- meaning "to be foul; contaminated;" polluted.  The writer also uses the terms "detestable" and "abhorrent".  Along with the list of things that could or could not be eaten, there are examples of things that would cause a person or thing to be temporarily unclean when they were touched.

What can we learn from this?  What does this matter since Jesus came and since Peter's vision on the roof in Joppa ( Acts 10) ?  

Verses 43-44; 47  " Do not render yourselves detestable through.... and you shall not make yourselves unclean with them..... For I am the Lord you God.  Consecrate yourselves therefore, and be holy; for I am holy.....  to make a distinction between the unclean and the clean.... "

First of all, we need to know that when we associate or partake of the things that are detestable and unclean in God's sight, that we make ourselves detestable and unclean.  We do this to ourselves.  It is a choice we make out of our own free will.
Most importantly,  these choices separate us from the will of God for us, which is, " you shall be holy for I am holy."  God desires us to be consecrated  to Him.  Set apart for Him.  Pure for Him. 

These 2 facts have not changed:
Unclean things make us unclean.
God desires us to be holy. 

No, we do not worry about what animals we can eat or not eat.  For God has provided everything.
Nor do we observe the various requirements for becoming clean again.  For Christ has made us clean!
Praise God!!
But, as Paul wrote in I Corinthians 10:23 " All things are lawful, but not all things are profitable."
We are exhorted by Peter  to be  " like the Holy One who called you , be holy yourselves in all your behavior." ( I Peter 1:15) How?  " As obedient children, do not be conformed to the former lusts, which were yours in your ignorance." ( verse 14)
Jesus told the Pharisees that is was not that which they ate or how they ate that made them unclean, but what came out of the heart.. 
Peter writes, " Therefore, putting aside all malice and all guile and hypocrisy and envy and all slander...."( I Peter 2:1)  And Paul tells us that the deeds of the flesh are " immorality, impurity, sensuality, idolatry, sorcery, enmities, strife, jealousy, outbursts of anger, disputes dissensions, factions, envying, drunkenness, carousing, and things like these...."  ( Galatians 5:19-21)
These are the "unclean" and "detestable" things that come out of the heart and render us unclean. 
These are some of the things that keep us from being holy as God desires us to be. 

As the Israelites could choose or not choose to partake of that which was unclean,  we choose to partake of the "deeds of the flesh"  or not.  Both Peter and Paul give instructions to help us make the right choice.
I Peter 2:2-3 " like newborn babes, long for the pure milk of the word, that by it you may grow in respect to salvation, if you have tasted the kindness of the Lord."   We must read and study and feed on the Word of God. It is our daily bread. Without it we will be weak and vulnerable to craving that which is unfit for a holy child of God. 
Paul writes in Galatians 5:16 " But I say, walk by the Spirit and you will not carry out the desire of the flesh." And in verse 25 "If we live by the Spirit, let us also walk by the Spirit."  We need the "living water", the Spirit of God constantly and consistently filling us and producing in us His fruit, "love, joy, peace, patience, kindness, goodness, faithfulness, gentleness, self-control;.." (v.22-23)

So, the issue of what is clean and unclean; polluted or pure; detestable or holy;  isn't what comes from outside of our bodies as it was for Israel, for it is what is in our hearts - our spiritual diet that matters. The principle has not changed.  There are still things that render us unclean in God's sight when we choose them instead of HIM. And He wants us wholly for Himself ! He loves us and desires for us to be like Him so that we can be with Him forever.  

Loving Father, You are holy and we exalt You.  You have chosen to love us and to redeem us from all sin and uncleanness. You have provided for our atonement through the cross of our blessed Savior, Jesus Christ.  You have given us Your Spirit to lead us in holy living, to fill us with all that is pure and good and acceptable. You have given to us the Word of Life . The Bread that provides true life.
Thank You.  Forgive us Lord for our trespasses and sins.  Cleanse us from every secret or hidden sin. May we grow in our knowledge of You and of Your Word and live a life worthy of You.  We ask in Jesus' powerful Name.  Amen.