Its like how Christians have many services to repent, Jews do it all in a day. Basically, we confess our sins and ask God to forgive us for them.
You have to fast for 25 hours, but at the end families usually have a very large meal. Children under 13 are exempted from fasting, and if you need food/drink to survive (if you need to take an important medicine, but need a meal for it to work), that's OK.
It's a pretty big list of things in the prayer for confession, so here's a link:http://www.chabad.org/holidays/JewishNewYear/template_cdo/aid/6577/jewish/Text-of-Al-Chet.htm