Rebbe Nachman taught: The 49 days of Sefirat Ha'Omer correspond to the 49 gates of teshuvah, as I mentioned in a previous post. These 49 Gates, in turn, correspond to the 49 letters which make up the names of the 12 tribes of Am Israel. Thus, each tribe has individual gates for each of it's members, so that everyone can return to Hashem through his own gate. And then there is the 50TH Gate, the highest gate: SHAVOUT. This gate is, as it were, the TESHVUAH, "The Return", of Hashem.
The way for a person to to come to his individual gate is through the Tehillim. Thus, during the 49 days of Sefirah, as well as on all other days of repentance i.e. (The month of Elul, Rosh Hashannah), we should recite Psalms. This will be us to our gate of repentance. And by achieving this, we will merit purity and coming back to Hashem.
That these day are a most amenable time for reciting Psalms and repenting can be learned from the begining of the book of Shemos. The verse reads, "these are the names of the children of Israel who went down to Egypt; each man and his wife, they came." In Hebrew, the last letters of these words make up the words Tehillim and Teshuvah. The verses which follow then list the names of the Tribes (their 49 letters). They correspond to the 49 days of Sefirah, corresponding to the 49 Gates of Teshuvah (Likutey Moharan II, 73).
