Well, hmm.
The devil here is in the details, so let's get those straight first.
Capitalization. iii is different than III. iii is minor, III is major.
Let's take our example into the key of C. If we are playing in C Ionian, E is the 3rd, iii, (and not very likely part of the progression). If we're in A Aeolian, however, E is now the 5th, III, and thus a secondary-dominant.
Why?
Resolution.
The tritone interval between the major 3rd and minor 7th of a dominant chord creates tension that begs to be resolved. So, the 3rd of "E" (G) is raised to G#, which then creates the necessary intervallic tension needed to bend our ear toward the root, A minor.
Clear as mud?
