The Greek word for "repent" is "metanoia" (noun) and "matanoeo" (verb) you see as defined in the Strongs #3340, 3341: to think differently or afterwards, reconsider. After thought, change of mind. Repentance basically means a "change of mind" and the context must determine what is involved in this change of mind. Where salvation is in view, repentance actually precedes saving faith in Christ and is not a totally separate act from faith. It is actually the same coin with two sides. Repentance is on one side, "what you change your mind about" and faith in Christ is on the positive side, "the new direction of this change of mind." *Repentance and faith are two sides of the same experience of coming to Christ (Acts 20:21).
In the context of Luke 13:3, Jesus challenged the people's notion that they were morally superior to those who suffered in such catastrophes. He called all to repent or perish. For some people though, prior to coming to the end result of repentance in receiving salvation (faith in Christ), they must change their minds about other specific things in order to get there. Repentance, metanoia, focuses on changing one's mind about his previous concept of God (as in Acts 17:30) and disbelief in God or false beliefs (polytheism and idolatry) about God (see 1 Thessalonians 1:9). On the other hand, this change of mind, focuses on the new direction that change about God must ultimately take, namely, trusting in Jesus Christ as the ALL-sufficient means of our salvation.
Certain people misunderstand the term "repentance" to simply mean "stop sinning." That is not the Biblical definition of repentance. In the Bible, the word "repent" means to "change your mind." The Bible also tells us that true repentance will result in a change of actions. Acts 26:20 declares, "I preached that they should repent and turn to God and prove their repentance by their deeds. "This is the fruit of repentance (Matthew 3:8), not the essence of repentance (change of mind). Certain people confuse the "fruit of repentance" with the "essence of repentance" (and also do the same thing with faith) and end up teaching salvation by works.
I have heard certain people say, "If you want to be saved, repent of your sins, turn from your sins." If turning from your sins means to stop sinning, then people can only be saved if they stop sinning. And in that case, it is unlikely that anyone will be saved, since we don't know anyone who has ever "completely stopped sinning" and lives a sinless, absolute perfect life, 100% of the time.