A mnemonic is a memory aid for something, often taking the form of a rhyme or an acronym. I before E except after C, is a mnemonic to help you remember how to spell words like "piece" and "receive."
As an adjective, mnemonic describes something related to memory. "Spring forward, Fall back" is a mnemonic device to help you remember which way to set your clocks for daylight savings time. Set the clock forward an hour in the spring when daylight savings time begins, and set the clock back an hour in the fall when it ends. Well-known mnemonics exist to help you remember things like the planets, the digits of Pi, and the color spectrum.