There are two generations of chips, so just talking about i3vsi5vsi7 won't always make sense. There are also mobile versions, so you have to compare like generations and versions.
in general i3's are dual core CPUs, i5's are quad core CPUs, and i7's are quads with hyper threading. There are also hexacore i7's.
In general a i7 will be more powerful than an i5, and an i5 more powerful than an i3. A low end 1st generation i7 might be less powerful than a top end 2nd generation i5
EDIT: the whole scheme is just extremely confusing