Economics. Suppose you have a factory and a growing order book but you're running at or near full capacity; if you get any substantial increase in the number of orders, it's going to take longer and longer to fulfill them, and customers might start to go your competitors if they feel the quality of your service has dropped. This is a diseconomy of scale - you've run out of room to grow and the more business you get the lower your margins.

The obvious solution would be to set up another factory. Suppose for simplicity that this costs $25 million and allows a doubling of capacity. suppose further that TeeSpring is making a profit of $100,000 a week (a completely imaginary figure - I know nothing about their finances). Because it's near full capacity that weekly net isn't going to increase much. But saving up the money to purchase the factory outright would take 4-5 years - an organic growth strategy - is plenty of time for competitors to move against you and pull away customers.

So you have a couple of options. You could go into debt, either by getting a loan or issuing a bond that pays interest (effectively the same thing). Now some of your income goes on interest payments, but they're tax-deductible and after you've paid off the debt you'll still have the second factory. As long as the increased income resulting from the investment is greater than the cost of borrowing the capital then going into debt can be perfectly sensible - the same reason it makes good sense for governments to splurge on necessary infrastructure during periods of low interest rates, just like we're not doing now due to politics :-/

Another option is to issue equity, ie sell shares in the company to raise the money. For large firms this may not be any more attractive than debt, because shareholders will expect a dividend of some sort. For growing firms it makes a ton of sense because early investors are not so much interested in dividends as in the possibility for the shares to appreciate in value - who wouldn't have liked to invest $1 million in Google or any other large company back in the early days? This is ideal for a firm like Teespring that has a very simple and straightforward business model - manufacturing a basic consumer product like this is great from an investor's POV because it's so easy to analyze.