(Assuming here that you're talking about C/C++.)
An inline function has its code copied into the points where it's called, much like a macro would.
The big reason you would use inline functions rather than macros to accomplish this is that the macro language is much weaker than actual C/C++ code; it's harder to write understandable, re-usable, non-buggy macros. A macro doesn't create a lexical scope, so variables in one can collide with those already in scope where it's used. It doesn't type-check its arguments. It's easy to introduce unexpected syntactic errors, since all a macro does is basically search-and-replace.
Also, IIRC, the compiler can choose to ignore an inline directive if it thinks that's really boneheaded; it can't do that with a macro.
Or, to rephrase this in a more opinionated and short way: macros (in C/C++, not, say, Lisp dialects) are an awful kludge, inline functions let you not use them.
Also, keep in mind that it's often not a great idea to mark a function as inline. Compilers will generally inline or not as they see fit; by marking a function inline, you're taking over responsibility for a low-level function that most of the time, the compiler's going to know more about than you are.