In Matthew 5:39, Christ said "Do not resist an evil person. If someone strikes you on the right cheek, turn to him the other also". I don’t understand what He meant?

"Resist not evil." in Matthew 5:39, simply means "do not retaliate to harm the person who hates you." There is nothing wrong with being angry when someone lies about you, etc. Ephesians 4:26 says "Be ye angry and sin not: let not the sun go down on your wrath." We wouldn't be normal if we didn't get angry; but, we are not to sin by letting the anger cause us to attempt harm towards our adversary. Neither should we let it fester in our minds for weeks and months. In other words, stay away from the person! Romans 12: 19 tells us "Dearly beloved, avenge not yourselves, but rather give place unto wrath: for it is written, Vengeance is mine; I will repay, saith the Lord". (Also read l Corinthians 5:11; II Corinthians 6:14-17; II Thessalonians 3:6,14,15).

Notice, in Matthew 5:29,30, we are not to literally "pluck out our eye" or we would all be blind. Nor are we to cut off our hand, literally, or we would all be walking around with stubs!. If we are enticed to sin with something we are looking at, then pluck our eye out from looking in that direction and look elsewhere. The same with our hands. Withhold it from whatever bad thing we are thinking of doing with it.

Read the rest of Matthew 5. It reveals that we are to love by not retaliating with hatred to do harm. It takes a mature Christian to do this. Sometimes we have to ask God for strength to love the unlovable! The word "perfect" as given in 5:48 means "mature". We have to remember that our Lord also suffered unjustly. " For Christ also hath once suffered for sins, the just for the unjust, that he might bring us to God, being put to death in the flesh, but quickened by the Spirit:"