Del is just the contraction of the preposition de and the singular masculine article el. Since you're talking about the distance from a certain supermarket, you would say "el supermercado", but since you need a de in front, it becomes del.
There are only two contractions in Spanish: del, and al, which is made from the preposition a with el.
Jmiex, del is a contraction of de and el, and al is a contraction of a and el. Prepositions get used for many things and I'm too tired to list them, but generally de means "of" (marking possession) or "from" (marking a starting point), and a usually translates as "to" (marking recipients and goals).