#import and #include are preprocessor directives for bringing in the contents of a header to a file. #include is replaced by the contents of the header directly, while #import is only replaced by the contents of the header the first time that header is imported.
Objective-C headers should be brought in via the #import preprocessor directive. Usage of #include should be reserved for C and C++ headers which, by convention, have #include guards. C and C++ headers may affect or rely on the preprocessor state, such as the use of #pragma push_macro, #pragma pop_macro, and x macros, which are not patterns conventionally used in Objective-C. Avoid #pragma once in Objective-C code as it is a non-standard extension and redundant with #import.
Using #import eliminates the need for #include guards, which are not used by convention in Objective-C headers. #include is the conventional directive for C and C++ headers and should be used so the headers are preprocessed as intended by the author.
#include "XYZObjcClass.h" // bad: possible duplicate inclusion of this header
#import "XYZObjcClass.h" // good: clang determines if this header has been included already and avoids duplicate inclusion
#import "XYZPreprocessorModifier.h" // bad: may not be inlined here to affect the preprocessor state
#include "XYZPreprocessorModifier.h" // good: preprocessor modifications reliably copied where needed
#import "XyzCppHeader.h" // bad: using Objective-C convention for C and C++ headers
#include "XyzCppHeader.h" // good: use proper convention for C and C++ headers