When listening to various pop opera or opera pieces, I sometimes hear the singer make their voice suddenly 'more masculine' for a particular part of the song.
I'm not quite sure how to describe it, so here are some videos (and the time) when these occur.
At 0:57
At 2:58
'Is there a name for this technique?
I'm not familiar with any specific name that technique has, and, really, it's a rather subtle thing that I wouldn't call a distinct technique in itself.
You may hear this variously described as having a "darker" tone, or sometimes as being "throatier". What these singers are doing is opening up the back of the throat more (lifting their soft palate and lowering the back of their tongue to create extra space).
Notice that in both cases, they do this right when they go to a higher place in their range. Opening up like this helps give them better tone and can help them keep from going flat, or from having to flip into head voice or falsetto. This isn't the only time you'll hear this change, but it is a rather common place to do it.
The word that I have heard used for this technique is "covering," as in "he shifted to a more covered tone for that high note." As Greg noted, it involves manipulating the resonance chambers of the throat to change the formant structure of the vocal tone.
This sound comes from lowering the larynx slightly, which lengthens the tube from vocal folds to mouth, and lowers all the overtones regardless of the pitch of the fundamental.
Lowered larynx sounds like rocky balboa Raising the larynx sounds like minime
And you're right it sounds more masculine because men have a longer distance from folds to mouth.
