Shevat is the eleventh Hebrew month (counting from the month of Nisan). On the current calendar it always has 30 days, making it a full month. As with all the Hebrew months, the name was adopted sometimes during the Babylonian exile. However, it is mentioned by name in scripture:
Zechariah 1:7 Upon the four and twentieth day of the eleventh month, which is the month Shebat, in the second year of Darius, came the word of the LORD unto Zechariah the son of Berechiah, the son of Iddo, the prophet, saying -
The month of Shevat is traditionally considered a month in which one is to return to the Torah. In Deuteronomy 1:1,3 we read:
These are the words which Moses spoke unto all Israel beyond the Jordan in the wilderness...in the fortieth year, in the eleventh month, on the first day of the month.
Here Moses is reciting the words of Devarim (Deuteronomy) to the children of Israel. He reviewed many of the teachings and instructions given at Mt. Sinai and in the wilderness. He also rebuked them for their rebellion against Adonai during their wilderness journey. He reminded them of the many rewards that they would receive if they remained faithful to Torah but of the awful punishments that would come their way if they did not keep Torah. In addition, he prepared them for the conquest of the land that would come under the leadership of Joshua.
Since Moses began his sermon on the first day of Shevat the sages compare it to the day of the giving of the Torah at Mount Sinai on Shavuot (Pentecost). On both of these dates Adonai appealed to the people (through Moses) to be obedient to the Torah. Tradition says that Moses preached what we call the book of Deuteronomy to the people for 37 days, until Adar 7, so Shevat is considered an appropriate time to renew and return to Torah.
There is also a national holiday in the month of Shevat called Tu B'Shevat on the 15th of the month. This commemorates a new year for trees. This was traditionally the date selected when the tithes from fruit trees were due to be given to the priests. It is a custom for children to plant trees during this month in Israel (or to donate money for that purpose). It is also traditional to eat new fruit from the land of Israel on the 15th and to recite a blessing over fruit trees.
One day in the future Torah will go forth from the holy mountain when Messiah Yeshua returns and all nations will flow into it. At that time the land will flow with milk and honey; an abundance of all things (Isaiah 2:1-3 and Micah 4:1-2).
(All scripture is from the JPS)