Sin is any action or thought done in disobedience to God.
When we disobey God, we sin.
When we say that we "repent our sin", it means that we have changed our thoughts and actions in a way such that we obey God in the future. However, it is impossible for us to perfectly obey God (and thus not sin). Thus repenting is on on-going process (daily) in which we continually turn away from sin whenever we discover we are sinning.
Unfortunately sin is a part of us:
"for all have sinned and fall short of the glory of God," (Romans 3:23 NASB)
That is why we need Jesus Christ. It is through Jesus that we are cleansed of our sin, being made clean enough so that we can enter heaven:
"For God so loved the world, that He gave His only begotten Son, that whoever believes in Him shall not perish, but have eternal life." (John 3:16 NASB)