“Then cometh Jesus from Galilee to Jordan unto John, to be baptized of him. But John forbad Him, saying, ‘I have need to be baptized of Thee, and comest Thou to me? And Jesus answering said unto him, ‘Suffer it to be so now: for thus it becometh us to fulfil all righteousness.’ Then he suffered Him.” Matthew 3:13-15 (KJV)
Coming to John the Baptist for baptism; these are the first words of Jesus spoken in the Gospel of Matthew. The baptism of Jesus was for the purpose of fulfilling the righteousness of God. Jesus certainly did not need to be baptized; except for that purpose. John recognized it and baptized Him.
Since the first words of Jesus recorded in Matthew were concerning righteousness; I would believe that righteousness is a very important part of Christian living.
Righteousness is doing the godly thing. The right thing. Thinking and acting Biblically in a corrupt world. If you are living like the world; you are not living righteously.