I've seen singers do that onstage and on TV over the years, the Bee Gees were the first ones I saw I think, and I wondered why so I tried it myself and found out I could really hear myself a lot better. I rarely am able to use this technique onstage myself, I'm usually playing guitar too so both hands are busy. After being onstage with really loud bands off and on for 30 years a lot of the time I think it may be because they can't hear themselves in the monitors.
With a band I played in years ago that was my signal to the sound man for more monitor. If my finger went to my ear he knew I could not hear the monitor. If I then pointed at someone else I could not hear them. That made our stage mix lots better, and having a great sound man I knew I didn't have to worry about what it sounded like out front, he refused to settle for less than the very best sound quality he could get at a good, solid volume level but not overbearingly loud. Boy do I miss that guy! The few chances I had to step out front of the mains I could hear every little sound...snap my fingers into the mic and you could hear it out front. You could even hear a whisper. And our cover tunes sounded like listening to the album, the mix was that good.
That makes a huge difference to a singer, if you can't hear what you're doing you have no idea whether you are hitting the right notes or not. Same for instruments as well, if I can't hear my guitar I have no idea what I just played. I've tried playing sax when I couldn't hear the thing, that really sucked...sure I know what notes I played, any certain key combination only plays one note, but I couldn't tell if I was in tune or not. And not being a great sax player by any stretch of the imagination a lot of the time I'm not sure what notes will work to begin with. That's even a bigger problem with harmony vocal parts, hearing all the vocal parts is then crucial. My note has to be right and in tune or the whole thing sounds terrible, same for everyone else.
In reference to a comment made above, I've always thought my voice sounded terrible too. Other people think it's good, some even say great but I've always thought they didn't know what they were talking about, to me it sounds awful. I'd rather keep my mouth shut a lot of the time...shut up and play your guitar!