Interstitial has to do with small spaces, called "interstices." Interstices can be literal spaces, like the gaps between your teeth, or they can be figurative, like the few minutes you have between classes.
You'll notice that when the noun interstice becomes the adjective interstitial, the -ce- changes to a -ti-. That's a fairly common spelling shift — difference becomes differential, for instance, where the -ti- is actually pronounced like -sh- or -ch-.
Close your vocabulary gaps with personalized learning that focuses on teaching the words you need to know.