It's worth starting by noting that when we talk about what the stock market does, we're talking about something we believe, not something that's necessarily true.
That said, we believe long term interest rates are correlated with economic growth. If the growth rate decreases, the P/E multiple of the market has to go down (because earnings growth is in the numerator of a discounted earnings stream, and earnings growth will be related, over the entire market, to overall economic growth). Also, when companies finance by borrowing, which they all do, earnings will be lower if interest rates are higher (for each non financial company, in this case). Finally, higher interest rates make financial assets other than equity more appealing, although I personally think that effect is far smaller than the earnings effect.