Curare is a non-depolarizing neuromuscular blocking agent. It sits on the receptors in the neuromuscular junction (where the nerve meets the muscle) and doesn't allow acetylcholine to activate those receptors, thereby paralyzing the muscles.
It is no longer available (at least not in the US) and we have better drugs that do the same thing. Curare releases histamine, so it was no good for asthmatics and it had other undesirable side effects. In fact, when it was available, it was mainly used as a defasciculating drug before succinylcholine administration. (Sux makes muscles twitch before it works, because it is a depolarizing NMBA. Curare blocked the twitching.) It could also be used as a paralytic during surgery, and was a fairly long-acting drug, but the histamine release and vagolytic effects made it a poor choice once other drugs were introduced. (I trained when the better drugs, like pancuronium and vecuronium, were already in use, so curare was never a first-line drug for me.)
Now, we use drugs related to curare - most of them have "cur" in their names: vecuronium, pancuronium, cisatracurium, rocuronium, etc. They have been chemically engineered to have fewer side effects and different durations of action. Succinylcholine is a very short acting NMBA, and has specific uses in anesthesia.
Although we say "relax", what it really does is provide complete paralysis of skeletal muscles. That includes the diaphragm, so it prevents breathing. When we use drugs similar to curare, we have to ventilate the patient.
I used to use curare, back in the day.