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It's based on the equity the investor is purchasing in the investment. Here's an easy math example:

I invest $10 in a lemonade stand and get 10% equity in the company. That means that I can theoretically buy the company at $100 to get 100% of the equity.

So when investors put $150M into a company, they are purchasing equity/stock/shares/whatever and the company can then be valued based on the percentage of equity they get for their investment.

Doesn't this just mean that Discord received 150 million in return for 7.5% stake at the company?

More or less, with the very big caveat that the specific terms of the deal means it's almost never actually a straight exchange of money for share of equity.

I would venture it's the huge amount of monthly active users. 200M users at just $1 a year (or month) is a lot of money compared to the $150M they just picked up in debt.

Potential future revenues and value...