The "dere" types are used to archetype the way an anime character deals with having a crush on another, "dere" meaning "lovestruck".
Crushes aside, dere types have made their way to be describe how someone acts casually as well, not just when infatuated.
There are many dere types, and if someone knows another, feel free to mention it, but for now, we will stick with the 5 most popular:
Deredere - This dere is the typical happy-go-lucky type and are not shy around their person of interest.
Tsundere - The tsundere is easily flustered and denies any interest in their crush with aggressive, and, in extreme cases, violent, responses. They will eventually warm up however (which is where the -dere comes from)
Yandere - The yandere is someone who obsesses over the other so much that they are willing to harm or even kill anyone who appears to be closer to their love interest than they themselves are. In most cases, they hide this by acting like a deredere near their crush.
Kuudere - A kuudere is someone who appears cold, stoic and emotionless. In some cases, they eventually warm up.
Dandere - The dandere is often confused with kuudere, but their difference lies in that the dandere is really just shy, bashful and avoids social interaction. While the kuudere is cold, just like that.
Additional "deres":
Himedere/Oujidere - The himedere is a character that demands they be treated as a princess, especially by their love interest. They are often portrayed as being arrogant and selfish at first, but might open up to their person of interest.
The oujidere is the male counterpart of this type.
Kichidere - This dere describes a character that acts insane, expresses feelings in a cutesy way, and likely will develop into a deredere over time.
Nyandere - Describes a character who acts like a cat, adding "meow" or "nya" to their speech. Also attributed to being clingy.
Kekkondere - A dere that is adamant on getting married right away.
The UCP is totally a kuudere, they keep a pokerface at all times but I know what they're thinking!