Simple machines are defined by their ability to redirect or multiply force, and Archimedes wrote the first known treatise on the subject in the 3rd century BC. It was he who codified the force-magnifying properties of the lever, with which, he famously claimed, he could move the world, if someone only gave him a place to stand.
In nature, the lever is the basis of nearly every aspect of the musculoskeletal system. If you have bones and joints, then you've got levers and fulcrums (the stationary parts of levers). There are three classes of levers defined by where the fulcrum, the load to be moved, and the initial force are placed along the lever's length. The most common lever in the human body is class 3, where that the force is applied between the fulcrum and the load, as in a catapult.
In the example of the bicep curl, the forearm is the lever, with the hand as the load and the elbow as the fulcrum. Between them is the bicep muscle, whose contraction provides the force necessary to swing the hand up. Class 3 levers don't make lifting the load easier--that's the domain of class 1--they increase the velocity of the action.
So those class 3 levers, like arms and legs, allow us to move much faster than we otherwise would.