I live and shop in a Mexican neighborhood. Main things I find at my grocery:
A large selection of chile peppers, both fresh and dried. In the fresh section, off the top of my head: serrano, poblano, jalapeno, habanero, anaheim, cascabel, banana pepper, peron (aka rocoto). In the dried: ancho, pasilla, guajillo, morita, chipotle, habanero, pequin, arbol, japanese.
The fruit and vegetable selection may be different. For example, at my store you will find fresh tomatillos, guava, various mangos, prickly pear paddles (nopales), prickly pear fruit (tuna and xoconostles), a selection of different types of plantains and bananas, fresh garbanzo beans, sometimes fresh fava beans, chirimoya, chayote, etc. Lots of different root vegetables including name, malanga, yuca, boniato, yautia, etc. The herb selection will definitely include cilantro, but often also epazote, maybe culantro, fresh chamomile, hoja santa (although not around my parts) and things like that.
The meat section may feature parts of the animal you’re not familiar with. There are often various types of tripe on sale. Skirt steak (both inner and outer) is usually a featured cut (outer skirt is generally preferred). You may have goat on sale. You may even find a goat or pig head on sale, depending on the time of year and how “hardcore” your Mexican grocery is.
Also, the butcher section may have homemade chorizo (sometimes both red and green varieties) and pre-marinaded meats of all kinds for grilling or roasting.
The dried herb section will usually be a bit different than your standard US herbs. Annatto seeds, Mexican oregano (quite different than regular oregano–they’re not even in the same plant family), dried hoja santa, dried shrimp (both pulverized and whole), etc.
You should be able to find masa (a hominy dough) or masa harina (flour made from hominy) that is used for making corn tortillas and tamales. Also, as said above, your tortilla selection should hopefully be better than at a regular grocery. My store doesn’t make their own tortillas, but they get deliveries from several different tortillerias in the vicinity, so when you buy them, they’re still warm in their wax paper.
If the grocery also contains a bakery, then you will find all manner of delicious Mexican sweets and some of my favorite rolls in the world: the telera and bolillo.
And that’s just off the top of my head, but your grocery may be different. Why don’t you just venture in and check it out?