I’m a lover of Yucatecan food, and recommend (with thanks to KimDDD for some of the descriptions - you can see her video in this post about dining Yucatecan in Mérida).

- Cochinita Pibil: Pork marinated in a citrus sauce which is then slowly cooked underground. “Pib” is the traditional Maya underground oven.

- Pescado Tikin xic (TEEkeen sheek): Whole fish marinated with achiote (annatto) paste and sour oranges wrapped in a banana leaf and cooked in an earth oven beneath a wood fire.

- Poc chuc (poke chuke) Pork in citrus marinade, cooked over a grill, often served with a side of rice, pickled onion, refried beans, and avocado.

- Queso Relleno: A hollowed out ball of Edam cheese, which is then filled with meat and spices. The dish is then baked until the cheese is really melty and gooey.

- Relleno Negro: A stew that is really black, made with chargrilled chillies and lots of other spices, usually with turkey or chicken. It's not really spicy although it contains a lot of (mild) chile.

- Sopa De Lima: Delicious chicken or turkey broth highlighting strips of chicken, fried tortilla strips and the mild local lime.

- Panuchos, salbutes, papadzules, others.

A good introduction to Yucatec food, often based on Maya cuisine (but sometimes with Spanish influence) is FOOD Fun & Travel’s Yucatan Food & Mayan Food Mega Guide: 50+ Unmissable dishes link.

Not as easy to find in Cancún as fast and tourist food, but at least once, try

Antojitos Yucatecos: Av Yaxchilán, SM 22

Emara Antojitos Yucatecos: MZA 17 LTE 2 y 3, Xel-ha

Labná: Calle Margaritas #29 Mz 20 SM 22

Los Almendros on Ave. Bonampák Sur #60 (branch of Mérida restaurant by the same name) has a vast menu of Yucatec specialties

Xkat-Ik (shcot EEK) restaurant near the 7-11

The Mercado 23 market downtown is worth a visit for real Yucatec and Mexican food at very reasonable prices