Perce_neige gave the best indication, but I can't refrain imagine that during the floods the ancient blocks of flats at the bottom of the seven hills looked like islands. It seems that in the beginning of Rome, lower areas were more exposed to floods than today.
From this meaning of insula comes the English "isolated", the Italian "isolato", and so on. There are not floods or water around, there are streets that isolate/cut off a number of houses from other blocks of houses.
"A block" in English is the (often square) land between city streets. If something is 3 streets away, it is "3 blocks away". An insula is a group of buildings that typically takes up the full area between streets, therefore it is a "block" of buildings.