According to Thayer's Greek-English Lexicon of the New Testament, to obey (hupakouo--Strong's #5219) means (1) to listen or harken, as of one who, when there is a knock at the door, comes to listen who it is; or (2) to harken to a command, thus to be obedient to or submit to.  It derives from akouo (Strong's #191) meaning to hear, to attend to or consider what is or has been said.

For instance, Rhoda hearkened to Peter= s knock and went to the door (Acts 12:13).  The wind and the sea (Mt 8:27, Mark 4:41, Luke 8:25) and unclean spirits (Mark 1:;27) obeyed Jesus.  Children are to obey their parents and servants are to obey their masters (Ephesians 6:1-5).

In the same way, we obey sin when we respond to the lusts that it arouses in our flesh.  In Romans 6:12, Paul indicates the way sin gains its power to control us:

Let not sin therefore reign in your mortal body, that ye should obey it in the lusts thereof.

Sin, which already dwells in our flesh, knocks at the door of our will.  It asserts itself upon us by stirring up lust (epithumeo--#1937) or evil desire, thus asking (or demanding) to be listened to and obeyed.  (The word lust means to set the heart upon, long for, desire.  It derives from a word meaning passion (as if breathing hard), which word derives from another meaning to immolate or sacrifice by fire.)  Once we respond to the lusts or evil desires, we have submitted to the source of them, namely, sin.

However, if we learn to recognize the stirring of evil desire as the knock or command of sin, we can choose to not attend to or consider those desires.  We can decide not to listen, harken, or submit to them, and thereby refuse to give sin dominion over us.