The Gemara, in tractates Brochos and Eruvin, relates that Rabbi Yochonon says that it is better for a person to walk after (behind) a lion then after a woman…
Reb Levik Schneerson, the father of the Lubavitcher Rebbe, once gave some insight in to this saying. He explained:
It is well known that every month has its mazel; for example, Tishrei is the mazel of moznayim (the scale), Cheshvon is akrov (scorpion), the month of Av is mazel ari (lion), and the month of Elul is besulah (maiden woman). Rabbi Yochonon says it is better to go after the ari (the month of Av ) and do teshuvah in the month of Elul, than to wait and do teshuvah after besulah (the month of Elul), leaving your teshuvah to the “last minute” by waiting for Tishrei, for when Rosh Hashanah comes around one should already be ready to face the king.

There is a similar thought in the first Mishnah of Rosh Hashanah. The Tanna Kama says that Rosh Hashanah L’maaser B’heimah (Tithe for Livestock) is on Rosh Chodesh Elul, however Rabbi Eliezer and Rebbi Shimon argue and say that the Rosh Hashanah for livestock is on the first day of Tishrei.

One can say that the Tanna Kama believes that one who waits until the last minute to do teshuvah (waiting until the final month of the year, Elul), is like a b’heimah (an animal). However, Rabbi Eliezer and Rebbi Shimon say only one who waits until the first day of Tishrei is like an animal, but in the month of Elul one can and should do teshuvah.