You can call it a polyrhythm or polymeter beat with an artificial resolution. (lots of buzzwords there...)
What it is doing is actually increasing the tension by using a 3/8 accent pattern over a 4/8 beat, giving it a sped-up effect. So if you are playing a steady 4/4 beat, switching to this would create an expectation for the listener, and hinting that something is coming up after this. By using such rhythmic overlays, you can also enforce a certain flowing or hurrying feeling. Luser Droog gave a Tori Amos example and there are many many more (if only I can remember them). A similar drum intro from a Megadeth song again with strong continuation feel.
This, in my personal opinion, boils down to the drum sticking pattern that almost every drummer learns at some point. It can be found in THE book, Stick Control for The Snare Drummer by GL Stone.
If you apply this over the whole drumset, often right hand travels around the drumset while the left hand plays ghost notes on the snare. This hopefully answers why it's 3 over 4 type accenting pattern. Now you can also think of finishing the last four strokes by
RLLR (this is what I meant by the following paragraph, switching hands switches the accent)
If you just shift the very last accent to the right(to the last beat), that would give a different kind of expectation, but still hints that hey we are moving on to a speedy section. The last beat and the first beat of the next 4 bars give hints for repetition via two successive accents, so it's a safe way to flavor up the rhythmic pattern since there is no risk of leaking out of the 4/4 feel.
LR.. (makes it rather a drum fill)
You can also let the whole 3/8 pattern go over the bar line and resolve itself after 6 or 12 bars, and that would also create a different expectation (or complication). This is often used to reset the listener's RAM (as we call it internally), because often the audience enjoys a short period of contrasting rhythms by the bass player and the drummer, but get a little confused as to what to follow. If you can land on the theme again perfectly, the resolution is more powerful after so many bars of contrast.
...... over the bar line case.....
RLLR LLRL LRLL RLLR || LLRL LRLL <insert your favorite eight beat group here>
A common variant of this (for drummers) is to switch to a double-time shuffle with a minimum swing (every three note grouping is played with a slight triplet feel with the shuffle pattern) while still playing in 4/4.
Why the last part is 4/8 ? It depends on how you want to tie the last bit to the coming bar. You can keep going in an 6/8 song (this pattern is implicit in Waltz) you don't need to do anything. But if you are in a mainstream 4/4 situation, you have to place 12 or 15 beats in a 16 beat slot. It's up to you how you arrange them.
I tend to classify such patterns with the feel they give to the listener rather than the structure they have. Excuse my last example ;)
Amerie - 1 Thing
The producer probably used the same idea to connect the verses. Probably they came up with the chorus first and then made a song out of it (personal opinion).