As a first approximation, this is how much money it would cost to buy all the shares. You’d pay $SHARE_PRICE for each share and then own the entire company. Therefore the concept is a decent measure for what the market has decided the company as a whole is worth.
A company with 10x the market cap of a competitor is considered 10x bigger, because it would take about 10x as many dollars to acquire.
I say “first approximation” because if you actually tried to buy all the shares on the open market, then increased demand would drive the price up, and not everyone would want to sell right away. In an acquisition, the acquirer offers a deal where all shareholders get, say, 1.25x the current share price, but only if all shareholders sell all their stock. And the board of directors of the company being acquired can compel all shareholders to do so, if that’s in the best interest of the shareholders.
