To relieve is to ease a burden or take over for someone. An aspirin can relieve a headache, and a substitute can relieve the teacher who fell asleep on her desk after lunch.
Relieve comes from the Latin word relevare meaning "to help" or "make light again." An ice pack might relieve a pain in your elbow, but you can also be relieved of your duties if you get fired (or taken out to lunch). A thief might even relieve you of your wallet. Like thief, relieve is the rare word that actually follows the "i" before "e" rule ("i" before "e" except after "c" or when sounded as "a" as in "neighbor" and "weigh"). Aren't you relieved?