Its authors describe it best: "Suhosin is an advanced protection system for PHP installations."
What the Suhosin patch does is it sets some limits for particular resource usages, prevents some possible buffer overflows, protects against some common vulnerabilities, and so on and so forth. Full feature list is here. For the most part, it prevents others (and you!) from being able to do bad things on and to your server.
APC is the Alternative PHP Cache, an opcode cache for PHP, or as its developers describe it: "APC is a free, open, and robust framework for caching and optimizing PHP intermediate code." If your eyes just glazed over or you can't make sense of that last quote, you may now walk away.