Succinycholine, as its name might suggest, is a cholinergic agonist indeed. It acts on the neural plate of skeletal muscles, where it activates the muscle cholinergic receptors.
Phase 1 block due to succinylcholine thus occurs by activating so many receptors at once, that the whole muscle gets desensitized and therefore paralyzed. A corollary of that is that muscle will twitch during activation, thus accounting for the reason why people twitch shortly before becoming paralyzed after a succinycholine iv injection. This phase 1 block will resolve in 2-5 minutes.
Now an interesting phenomenon is that if you go on stimulating the muscle with more cholinergic agonists (for example, a second iv dose of succinylcholine), you may end up provoking endocytosis and degradation of the cholinergic receptors. This is called phase 2 block, and in contrast to phase 1, it will take at least several hours to resolve. This is why we never use a second dose in the clinics, except in very special cases.
You can also read about it all on wikipedia