Enterprise value answers the acquirer's question. If you bought every share you would also inherit the debt and get the cash, so the real price is market-cap plus net debt. It lets you compare companies with different amounts of leverage on the same footing.
It also explains why a heavily indebted company can look cheap on pe-ratio and expensive on EV multiples. Watch EV in any leveraged-buyout or merger story, since the headline offer per share is only part of what the buyer pays.
Example: 200M shares at $25 is $5.0B of market cap. Add $2.0B of debt, subtract $600M of cash, and EV is $6.4B, 28% above the equity value.
Related: market-cap, leveraged-buyout, deal-premium, book-value