What does Teshuva mean?

A Definition of Teshuva

Teshuva ( תשובה), commonly known as Repentance, is literally derived from the verb שב (to return). Teshuva is the central theme that reflects the month of Ellul, with Rosh Hashana and Yom Kippur being key dates in this process.

Rambam[1] writes in his work Hilchot Teshuva, that there are 4 steps to Teshuva, each of which are crucial for complete repentance.
1. Stop doing the sin
2. Regretting the sin
3. Vidui (confession)
4. Not doing the sin again

Step 2, regret, or guilt, should not be confused with shame. Whilst guilt causes negative thoughts and feelings about the sinful act in itself, shame reverts back to the person and can cause lack of self-worth, confidence and may ultimately result in depression. Rather than "I am ashamed and feel bad about myself because I did X", one should feel guilty and embarrassed about X itself.
Regret helps one's personal growth and spiritual development, shame does not.

Step 3, Vidui, is confessing directly to:

• Hashem; for sins that were "ben adam le makom" (sins against Hashem, e.g. chillul Shabbat[2], Kashrut, etc.)
• Other people; for sins that were "ben adam le chavero" (sins against people, e.g. lashon hara[3], treating individuals badly, etc.)

Vidui includes not only direct confession but also Mechila, asking for forgiveness. Asking someone for mechila is the hardest step in the Teshuva process.

Notes

[1] Rabbi Moses ben Maimon (Maimonides; 1135-1204), great Torah scholar, doctor, philosopher, or in the words of A.J. Heschel, "If one did not know that Maimonides was the name of a man, one would assume it was the name of a university. The writings and achievements of this twelfth century Jewish sage seem to cover an impossibly large number of activities". see here for more information.
[2] Desecration of Shabbat
[3] Evil speech or gossip