The word deal has several meanings:

1. To distribute or give out something, especially playing cards. When you deal cards in a game, you pass them out to each player. A dealer is the person doing the dealing.
2. An agreement or arrangement between people. When you make a deal with your friend to trade lunches, you're both agreeing to the exchange. Business people make deals to buy and sell things. Politicians sometimes make deals to support each other's proposals. A good deal means favorable terms: “I got a good deal on this bike.” A raw deal means unfair treatment.
3. To handle or take action on something. A principal might deal with a problem at school. When you deal with a difficult situation, you're managing it or working through it. This meaning suggests taking responsibility rather than avoiding the issue.
4. A large amount, usually in phrases like a great deal. If you care a great deal about something, you care very much. If someone talks a great deal, they talk a lot.

The phrase “big deal” can mean something important, or (said sarcastically) something that's really not important at all.