Undead is a term for creatures that are animated but not really alive -- usually they started out alive, then died, and then were somehow re-animated while not properly regaining life.
The exact mechanism of this re-animation depends on the setting; in fantasy worlds, there may be some abstract "negative energy" (as in Dungeons & Dragons) that can animate flesh that is no longer alive, while science fiction tends to invoke chemicals, electricity, or more advanced concepts like nanomachines that restore some semblance of life to dead creatures.
Though they may be capable of moving, and in some cases talking and thinking, the undead usually lack some characteristics of living creatures. For example, they may lack a heartbeat, or be cold to the touch, as their bodies no longer possess (or require) a metabolism. They are also sometimes said to lack a soul, which can manifest itself as being unable to cast shadows or reflections, as if they are lacking some substance required to do such things. Unquenchable hunger and thirst (especially for blood, souls, or other substances associated with life) are also common symptoms.
Historically, undead were seen as abominations; creating life from non-life was strictly the province of God or the gods, and mortals who intruded on that domain were evil, as were the fruits of their efforts; also that they're not genuinely restored to life, just an inferior and/or corrupt imitation of life. Over the last couple hundred years, opinion has shifted slightly; people who create undead, like necromancers, are still usually regarded as evil, but the undead themselves are usually at least pitied for having once been human and then made into monsters against their will.
An interesting thing that seems to connect many different types of undead is that they tend to serve either as examples of what happens should you fail to behave in a certain way (show the dead the respect they deserve, make sure you have your earthly affairs in order, don't be a murderous asshole) or attempts to explain the freaky shit the body goes through when decomposing (Rosy red and bloated? He's a freshly-fed vampire!).
Nevertheless, relations between the living and the undead are usually adversarial. In settings where undead are animated by "negative energy", they are usually automatically evil, with whatever intelligence they possess bent towards satisfying their hunger and becoming more powerful. The good-aligned undead like ghosts and necropolitans are unusual. Undead may be harmed by holy energy focused by clerics, or by any "positive energy" of any kind (e.g. healing potions or items).
The Chinese Communist Party is deeply afraid of undead for some reason, and works fervently to ban their depiction from media. The official line is something about it promoting superstition, but it may just be a fear the millions of people they killed will be back for revenge. According to some other sources it's actually because the Chinese culture has a lot of respect for the dead and so depictions of scary undead are seen as insulting. Though this can be a little confusing because they actually do have some scary undead in their folklore.
Types of Undead
- Bodak (if you count them)
- Death Knight
- Lich, intelligent undead wizards.
- Skeleton, known for being spooky and scary. One of them is inside you right now.
- Vampire, intelligent undead who vant to suck your blood and are occasionally obsessed with counting.
- Zombie, unintelligent, slow and clummsy. In a lot of media, contagious; this latter niche in D&D is taken by the ghoul.