A particularly valuable aspect of the term is that it lies on a spectrum of concurrent behavior, where thread safe is the strongest, interrupt safe is a weaker constraint than thread safe, and reentrant even weaker.
In the case of thread safe, this means that the code in question conforms to a consistent api and makes use of resources such that other code in a different thread (such as another, concurrent instance of itself) will not cause an inconsistency, so long as it also conforms to the same use pattern. the use pattern MUST be specified for any reasonable expectation of thread safety to be had.
The interrupt safe constraint doesn't normally appear in modern userland code, because the operating system does a pretty good job of hiding this, however, in kernel mode this is pretty important. This means that the code will complete successfully, even if an interrupt is triggered during its execution.
The last one, reentrant, is almost guaranteed with all modern languages, in and out of userland, and it just means that a section of code may be entered more than once, even if execution has not yet preceeded out of the code section in older cases. This can happen in the case of recursive function calls, for instance. It's very easy to violate the language provided reentrancy by accessing a shared global state variable in the non-reentrant code.