Daedra are beings that didn't help create Mundus as the Aedra did and so have their full power.
Despite what most of the populace of Tamriel thinks, the Daedric Princes aren't demonic or even evil. Their will is unknown and do not consider themselves evil.
When a Daedra is slain it doesn't die, its physical self is rendered innate but its souls returns to Oblivion and waits for a new physical form to take.
The Daedra are considered the best blacksmiths ever and they make the nearly indestructible Daedric armour and the incredibly strong Daedric weapons. Not all Daedra are capable of wielding them as most prefer to use their natural claws, teeth or magic. The Dremora are the only ones to use actual weapons and armour.
 Daedric Princes
Daedric Princes are the Lords of Oblivion and they each have their own Plane of Oblivion. Each of them are worshipped by many people and although it isn't illegal they prefer to live in secluded communities together.
They all have distinct personalities and some are not inherently evil. There are ones like Vaermina and Namira who are very dark and evil and there are others like Sanguine and Sheogorath who appear light hearted and like to drink and party.
 Lesser Daedra
There are a lot of lesser daedra that are in a lot of different shapes and sizes but the most recognizable are the Dremora. They are the foot soldiers of Mehrunes Dagon and are ranked, the most important being the Markynaz.