Why mark a method const, and what does it guarantee?

A const method promises not to modify the object's observable state, the compiler enforces this by making this a pointer-to-const inside the method, so any attempt to write a data member is a compile error. Two payoffs: it documents and guarantees that a query (like empty(), size(), peek()) is side-effect-free, and it's the only kind of method you can call on a const object or through a const reference. If you forget const on your query methods, any code holding a const& to your object can't call them, and that friction propagates through the whole API. So const-correctness is something you design in from the start: mark every non-mutating method const. (The subtlety: const protects the object's own members, not what a member pointer points at, for that you'd also need the pointee to be const.)