An acquisition usually means buying the existing shares. Since initial investors got their shares at very low valuation (roughly, "the stock price was low", though the company isn't publicly traded at that stage), a high-value acquisition usually buys shares for much more than the investor paid for them. That means the investor gains money.

The same goes for an IPO. In that case, the stock becomes publicly traded, usually at an initial price far above the valuation per share at the time the investor invested, and the investor can sell their stock for much more than they bought it for.

In broader terms: the investor owns part of the company as part of their investment. If the company becomes worth more, their share also becomes worth more.