Grievous is a Kaleesh cyborg from the planet Kalee, Supreme Commander of the Separatist droid armies, and the closest thing the Clone Wars has to a recurring monster. In current canon his first appearance is Revenge of the Sith (2005), where Matthew Wood voices him; the same actor carried him through seven seasons of The Clone Wars.
Mostly not a droid
The design invites the mistake and the story depends on you not making it. Grievous is a living Kaleesh warlord whose organic body was destroyed and replaced with a magnetised duranium frame, leaving little more than his brain, eyes and internal organs. That is why the Force does not flow through him and why he cannot be a Sith — he is Count Dooku's pupil in lightsaber technique and nothing more. Dooku trained him personally, which is the whole joke: he fights like a Jedi because a Sith taught him to, and he is not Force-sensitive at all.
The collection
He keeps the lightsabers of the Jedi he kills. It is the single most efficient piece of characterisation in the prequels — a trophy cabinet that tells you he understands exactly what he is not. The cough, added in Revenge of the Sith, was a late choice and does more work than it should: it makes an indestructible general audibly, permanently damaged.
The television rehabilitation
Revenge of the Sith gives him about eleven minutes and a humiliating death. The Clone Wars spent six years making him a credible threat again — sacking the Jedi Temple's defenders, capturing Ahsoka Tano, duelling Obi-Wan Kenobi repeatedly and losing to almost nobody except when the plot required it. Filoni's team also gave him the habit of fleeing the moment a fight stops being winnable, which reads as cowardice and is actually the only rational policy for a general who is a strategic asset.
The Legends version is a different character
This matters and is easy to get wrong. Genndy Tartakovsky's 2003 Clone Wars micro-series and the Legends comics give him an origin in which Jedi and the Republic engineered the shuttle crash that maimed him, making him a victim manipulated into service. That backstory is Legends and is not current canon. Canon's Grievous chose the reconstruction.
How he ends
Obi-Wan shoots him in the chest with a blaster on Utapau, then looks at the weapon with visible distaste. It is a deliberately unheroic end for a character built entirely out of melodrama, and it is the last beat before the Republic falls.