That's a great question. So, what you have to understand is that computer programs (such as a bitcoin wallet) come in two forms:

The first type of computer program is "Assembly Code". Assembly Code is basically a list of specific instructions for your computer to follow. In order for your computer to run a program, it needs to be assembly code. Different computers may have different assembly.

The second type of computer program is "Source Code". Source code is more of an abstract specification of what the program needs to do. In order to run source code, it must first be converted into assembly code using another program such as a "compiler" or "interpreter". So why use source code? It is a lot easier for programmers to create, review, and modify source code than assembly code. Additionally, source code can be used to make a single abstract program that can be translated into many different forms of assembly code: in other words, you won't have to re-write every program for every new type of computer.

An "Open Source" program is one where the makers of the program share the source code (not just the assembly code) so that others can review it as well as run it. Most of the commercial software you might encounter on a day-to-day basis is not open source, for example Photoshop or Windows or PayPal. However many alternatives are open source like Krita, Linux, or Bitcoin.

Another term you might hear is "Free Software": this basically means that the code is Open Source but also is released under a license that allows you to legally copy, modify, share it, etc. This isn't to be confused with "Freeware" which just refers to any program released at no cost (like WinRAR or Bonsai Buddy).

If you're looking for a secure program, you should choose one that is open source and heavily scrutinized, because there will be many programmers reviewing it for security vulnerabilities. However, many open source programs aren't well-reviewed, so be careful, and try to run the latest versions of the program so that you can take advantage of their fixes and security improvements.