Hanukkah is an eight-day minor Jewish festival occurring in December during which Jews light candles every evening. Some extra prayers are added to the daily prayers. It's customary to eat certain foods.
Ramadan is the Holiest Muslim month during which Muslims fast all month during the day. It happens every 12 lunar months and therefor can fall out anytime during the year; each year it starts about 11 days earlier than the previous year (on the "solar" calendar.)