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.

Equity investors only get returns through selling shares or dividends. As an early investor you prefer the company reinvest all profits (if any) into growing the business. Therefore, your return ONLY comes from selling shares. Angels tend to be wealthy and experienced investors. This allows them to be patient with their investments.

Early investors see the potential for a company before others. Most of its value lies in the future and its not tested yet. Products have to be made, code has to be written, employees hired, distribution deals signed, supply chains made, etc.

Angel investing is akin to flipping homes, you buy cheap homes, renovate them and then sell for a profit. You won't see cash until you sell the property.

As the company grows and gains more experience, more investors become interested and want a piece of the pie. The early investor could sell shares at this point, getting bought out, but they lose out on future earnings.

Angels are looking for returns multiples higher than their investment.

Why? Most startups fail.

If you have ten portfolio companies, chances are 7 will fail, 2 net a decent return and 1 becomes a hit.

Angel investors have to be willing to take huge risks and able to absorb losses.

Think of a business as an engine that is designed to generate money.

The business plan is the engine's blueprint.

But for the engine to actually run, you have to machine its parts, assemble them, test the engine, and make a few adjustments before it will reliably generate revenue. These require startup capital.

Engines also need fuel (cash). But the idea is that so long as it generates more cash than it consumes, then the engine does its job.

Angel capital is what lets a startup begin building the pieces needed for its money engine to run. Once the engine starts running, cash is diverted back to investors in proportion to what was agreed upon in exchange for their equity.

Even if the business is sold or acquired, the initial investors still retain their share of the business's output.

I buy 20% if a company for 1 million dollars. Now the evaluation of the company is 5 million.

The company goes public. It is now selling great in the market and the total evaluation is now 50 million.

If said investor sells all of his stock (20%) to people that want to buy it he now has 10 million. So he made 9 million total.

This is obviously not taking into account things like how him selling all his stock effect price, but we need to make it simple.

In an IPO, the shares that the angel investor owns is now traded publicly. Each share is now worth the open market share price and can be sold for cash.

If the startup is acquired, the amount the purchaser pays is distributed to the existing shareholders (angels, founders etc) according to the portion of shares they own.

Shares represent ownership. The buyer has to pay the owner to purchase. That is the straightforward concept.