He's referring to the mathematical formalism.

Sets of elements, ordered by the subset relationship, are a good example of a lattice. Lattices have a specific "top" and "bottom". Among the subsets of the letters in the alphabet, the empty set is "bottom", and the entire alphabet is "top".

The particular point of calling it a "lattice" rather than a ladder is that there are many ways to be more specific; of these, not all are more or less specific than each other. (Formally: you can have a < c and b < c such that neither a < b, a = b, nor a > b.)