Taken from: https://www.gnu.org/software/libc/manual/html_node/Nonreentrancy.html
For example, suppose that the signal handler uses gethostbyname. This function returns its value in a static object, reusing the same object each time. If the signal happens to arrive during a call to gethostbyname, or even after one (while the program is still using the value), it will clobber the value that the program asked for.
I fail to see how the above scenario is non-reentrant. It seems to me that gethostbyname is a (read-only) getter function that merely reads from memory (as opposed to modifying memory). Why is gethostbyname non-reentrant?
As the word says, reentrancy is the capability of a function to be able to be called again while it is being called in anothe thread. The scenario you propose is the exact place in which reentrancy is exercised. asume the function has some static or global variable (as the gethostbyname(3) function does) As the return buffer for the structure is being written by one, the other call can be overwriting it to completely destroy the first writing. When the in execution instance of the function (the interrupted one, not the interrumpting one) gets control again, all it's data has been overwritten by the interrupting one, and destroyed it.
A common solution to solve this problem with interruptions is to disable interrupts while the function is executing. This way it doesn't get interrupted by a new call to itself.
If two threads call the same piece of code, and all the parameters and local variables are stored in the stack, each thread has a copy of its own data, so there's no problem in calling both at the same time, as the data they touch is in different stacks. This will not happen with static variables, being those local scope, compilation unit scope or global scope (think that the problem comes when calling the same piece of code, so everywhere one call has access to, the other has also)
Static data, like buffers (look at stdio buffered packages) etc. means in general, the routines will not be reentrant.