This is a kind of cheese originally from Oaxaca, but now produced all over Mexico.
It is not very different from some kinds of mozzarella: it is produced in a long thin strip which is subsequently formed in a cheese ball. The ball can wheigh several kilos. In markets, vendors have a giant ball of quesillo: when you order your cheese they will unwind a length of it, and form a smaller ball for you.
Good quesillo has a distinctive taste, but it is not sharp. When it melts, it should produce very little "water". It has a fibrous structure, and you can actually shred it in long thin filaments with your hands (this is called deshebrar in Spanish).
Quesillo is also known as Queso de Oaxaca, and it is essential for making quesadillas. It is also used to make tortas.