When the Bible refers to fasting, it refers to abstaining from food and drink for a specific period of time. Fasting is designed to humble us, and draw us closer to God. It is not a form of penance or a way to attain favor with God through self-imposed suffering.
Fasting, by definition, is going without food and/or drink for a period of time. Typically, biblical fasting involves a person refraining from both food and drink, however, there are variations that may be done for health reasons.
Here is a wonderful fasting resource if you would like to read more before beginning your fast.