I work in medical research for a non-profit. Where your money goes depends a bit on if the non-profit is a big fund raising non-profit or if it's a smaller research group.

If it's a big fund raising non-profit then they will use some of the money for admin, but save most of it. They don't actually do any research themselves. People who are doing research will contact that company with their research proposal. The proposal includes a list of expenses and what they hope to achieve. They are competing with a bunch of other researchers doing the same thing.

The big non-profit will sift through all the projects then choose a few projects to fund. So they will give money to a smaller research group, and then the researchers go off and do their on thing for a few years. Sometimes they will give money only for one specific purpose, we once had a grant to buy a minivan but couldn't use that money on anything else. The way it works is a bit like a college scholarship where the researchers are mostly left alone to do their own thing for 5 years but have to give progress reports and are expected to accomplish something at the end of the study. Like a few published papers.

Smaller non-profits are the research groups, they actually have researchers on staff and will do research themselves but their research projects are usually not funded internally, they are funded by grants (see above). The grants pay the salaries of the researchers, but not the salaries of the admin (HR, accountant, marketing, stationary, supplies etc). That's what your donations to the smaller non-profit pay for.

If it's a big non-profit, they dont know what projects they will be fundiing until people apply for grants. If it's a small non-profit, they dont want to say "your $50 will pay for for our accountant to sit at their desk and figure out how to calculate my holiday leave" even though those jobs have to be done as part of research. Instead they tell you about previous research they have completed and papers they have published to prove that they do good research in general.