Great
Considerable, Important, Big Deal
adjective
した is the past tense form of する (which means "to do"). So, essentially this word is "did big." What is something that "did big"? It's something that's great or considerable.
たいした
The reading for the 大 part is actually the on'yomi reading you learned when learning this kanji. Since 大 has two on'yomi readings, here's a mnemonic to help you remember which one to use:
When something's great and important, you'd better wear a tie (たい) for it. No showing up without a tie to anything that's a big deal, okay?
それは大したことはない。
It’s not a big deal.
まったく大した女だよ。
She is such a great woman.
マクドナルドのしゃちょうになれれば大したものだ。
Being the president of McDonald’s would be a big deal.