Reposo is the "afternoon break" that Italians take. Pretty much everything closes down for a few hours every afternoon. Supposedly this is for taking a rest but every Italian I have asked says "we do NOT sleep!". So I suppose the rest is just a break from work or shopping. (Although they should be taking a nap after how late they all seem to stay up and how early they get up...)
In some ways I find this a very charming tradition. There is no way you could make Americans "stop" for a few hours every afternoon. But to Italians, this is part of every day life, part of their culture.
To be honest though, this tradition sometimes aggravates me. There are times when I have said to myself, "I will pick up ingredients for dinner after I eat lunch, on my way home", forgetting that everything will be closed. And then I have to make a trip back in to the store in a hurry, right before dinner.