It’s not a big deal.
She is such a great woman.
Being the president of McDonald’s would be a big deal.
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.
The reading for the 大 part is actually the on'yomi reading you learned when learning its kanji. So, as long as you remember that (and remember to use that reading), you can read this word as well. 大した = たいした.