What is 32-bit and 64-bit?

Can you explain the difference between 32-bit and 64-bit systems? I've heard them mentioned in relation to computers and software, but I'm not entirely sure what they mean. Specifically, how do they differ in terms of their capabilities, performance, and compatibility with other programs? Is there a clear advantage to using one over the other, or does it depend on the specific use case? I'd appreciate any clarification you can provide.