Interstitial has to do with small spaces, called "interstices." Interstices can be literal — as the gaps between your teeth, or 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-.
