The main fast day of the year is Yom Kippur, the Day of Atonement. Here, we are meant to concentrate on our prayer and repentance continuously throughout the day, and hence a break for a meal would firstly give us a break, and secondly, give us a reason to enjoy the day, which is contrary to its purpose.
Fast days are, in general, solemn occasions.

The other fast days during the year are:

• Tish B'Av
• The Fast of Gedaliah
• The Fast of Esther
• The Fast of Tammuz