What is the meaning of Matthew 5:43-44?

43 Ye have heard that it hath been said, Thou shalt love thy neighbour, and hate thine enemy. 44 But I say unto you, Love your enemies, bless them that curse you, do good to them that hate you, and pray for them which despitefully use you, and persecute you; (Matthew 5:43-44 KJV)

William Burkitt’s Commentary

Another corrupt gloss which the Pharisees had put upon the law of God, our Saviour here takes notice of: the law said,  Thou shalt love thy neighbor, Le 19:18 This they interpreted to relate only to their own countrymen, the Jews; concluding, that they might hate all the uncircumcised nations, as enemies; but, saith our Saviour, I require you to love all men; for if enemies must not be shut out of your love, none must.  

Love your enemies: here the inward affection is required.  

Bless them that curse you; there outward civility, and affability is required.  

Do good to them that hate you; here real acts of our bitters and most malicious enemies.  

Pray for them that despitefully use you, and persecute you: these are the highest expressions of enmity that can be, calumny and cruelty; yet are we commanded to pray for those that touch us in these two tenderest points, our reputation and sincere affection towards our most malicious enemies; to be ready upon all occasions to do good unto them, and pray for them.