Both anodes and cathodes are specific types of electrodes, which are simply conductors of electricity. Electric current (which is merely the movement of electrons) flows into an anode, and flows out of a cathode. See the first link for an in depth discussion.
A vacuum tube triode consists of both an anode and cathode, and additionally, a metal grid, which is an assemblage of wires that surround the cathode. The grid in turn is surrounded by the anode.
When power is applied, electrons congregate around the cathode and are prevented from moving towards the anode by the grid, which is more negatively charged than the cathode. Depending on the strength of the negative field of the grid, electrons may or may not reach the positively-charged anode on the periphery. See the second link for more details and a few graphics: