Updates
Shofar
Yesterday - Wednesday - was the first day of the month of Elul.
The next 40 days, from yesterday, correspond to the 40 days that Moshe (Moses) spent on Har Sinai (Mt Sinai), to receive the 2nd set of Luchos (Tablets with the 10 commandments written on them).
Moshe came down with these Luchos on Yom Kippur. Ever since, these 40 days are especially auspicious for Teshuva (repenting).
The custom is to blow the Shofar (Ram's horn) after Shacharis (the morning prayers) from yesterday, until Tuesday 28th Elul (7th September), as a reminder to start improving one's Torah observance and to repent for past misdeeds.
On Erev (the day prior to) Rosh Hashana (the Jewish new year), the Shofar is not blown, in order to create a break between the custom of blowing Shofar in the month of Elul and the Torah-commandment to blow Shofar on Rosh Hashana.
Source: Kitzur Shulchan Aruch 128:1, 2