FLEXION - basically means bending, more specifically movement where the angle at the joint is reduced. In the picture on the left, the biceps muscle is the flexor muscle when the muscle is "flexed"
EXTENSION - basically means straightening but increasing the angle of the joint. In the picture on the left, the triceps muscle is the extensor muscle when the arm is "extended"
Muscles in the body normally work in pairs, one is the PRIME MOVER (in this example this is the BICEPS and the other one holds it in check (the TRICEPS in this example).