Today, the 15th of November, the Orthodox Church starts the Nativity Fast. This fast will last for 40 days. Some people may call this fasting period Advent, which is slightly shorter in the West. During this fasting season falls such feasts as the Presentation of the Theotokos, and Saint Nicholas Day- when Orthodox traditionally gave gifts.
The Nativity Fast is less strict, for the most part, than Great Lent in that it allows for the partaking of oil and wine on most days until the 12th of December - fish is allowed on Sundays. From the 13th to the 24th is a strict fast with no oil and wine allowed except for on Saturdays and Sundays - no fish allowed during this time.
Much like Great Lent, this fast is also helping us prepare for the coming of a great feast; in the case of Lent we are preparing for Pascha, and in the case of this fast we are obviously preparing for the Nativity. During the fasting times, not only do we Orthodox fast from food and drink, but we also try to pray more and give alms.
We fast because "it is believed that by learning to temper the body's primary desire for food, that other worldly desires can be more easily tempered as well." (Wikipedia)
By fasting, we “shift our focus” from ourselves to others, spending less time worrying about what to eat, when to eat, how much to eat, and so on in order to use our time in increased prayer and caring for the poor. We learn through fasting that we can gain control over things which we sometimes allow to control us—and for many people, food is a controlling factor.
[We live in the only society in which an entire TV network is devoted to food!] While fasting from food, however, we are also challenged to fast from sin, from gossip, from jealousy, from anger, and from those other things which, while well within our control, we all too often allow to control us.
Just as we would refrain from eating a lot before going to an expensive restaurant for dinner—if we “ruin our appetite” we will enjoy the restaurant less—so too we fast before the Nativity in order to more fully feast and celebrate on the Nativity itself. (OCA.org)
We fast during this time so we can better focus on Christ and others around us (hence the almsgiving mentioned above). We fast so that the feast is all the more sweeter to us. We fast to help rid our bodies of temptation - for if we can resist food we can also resist other temptations.