Not about Stripe in specific as I haven't looked at their process yet, but some general information.
Advances are done on receivables generally and are not a way to bridge between rounds. The are a form of a short term loan and will be paid back as the receivables come in. The most common way this is done is you are given say 50-80% of the value of your receivables (varies depending on market and business), and any interest that might accrue during the collection period. Essentially this is selling your receivables for a discount to get cash now. I personally view this method as the equivalent of consumer payday loans, with much of the same high risk attributes.
Alternatively, there are some banks who will loan against receivables, using them as collateral, and that is almost always a better way to go as it is much less expensive overall, you still pay a higher interest rate generally but it is less crazy. But again, this is usually done as a cash flow management method, not to bridge between rounds. But this will be treated as debt against the company and likely the founders if you are small and haven't established solid credit for the company yet.
This is something I think most VC backed founders don't know, understand or learn. They don't establish credit with a couple of banks early enough when they have the funds. I always start building credit with banks early. Take $10k or some modest amount, use it as collateral for the bank to give you a loan in the companies name only. Then use the hell out of it paying it timely and never messing up. Then ask for a credit line increase to $20k or something along those lines after 6 months of solid use and good payments. Keep doing this over a couple of years and it is very easy to get $100-250k in line(s) of credit from banks and you only paid some modest interest on the way to get it. Then when you have the need that line is already there and it can be a huge difference maker, plus the key is you get rid of personal guarantees this way much faster than you would otherwise. It is crazy to me why startups don't do this regularly, it is very common in normal the SMB world and with serial entrepreneurs.