I've heard, that singing or humming notes while playing scales or arpeggios is good for you. Is that so? In what way? If I am not a singer, why should I be singing the notes?
Let me make it clear; I am no singer, but I have found it very useful to hum the notes of a scale/arpeggio when practicing them on the guitar.
One of the reasons why I do is if I hum the notes while I play, then if I was to go wrong, firstly I would hear that I had gone wrong, and then I would be able to go back to the point of my mistake, and be able to identify the note that should have been played from the corresponding note in the 'hummed' scale.
Secondly, it has helped me become much more aware of what the notes actually sound like. This helps loads when I am figuring out a chord sequence or riff to a song. I can hum the note/chord pitch from the song, and then be able to identify the general area of notes that that pitch is from, making it much easier to pinpoint the note/fret that is played.
Sadly, I cannot listen to a song, and hear a note, and be able to say 'oh, that's an F' immediately, but hopefully that will come with practice.
When you start trying to write or improvise you own tunes one good tactic (for some people...) is to sing the melody you want to play either in your head or out loud and try to mimic it on the fret board.
This is a two way street. If you sing out as you are practising you will develop a better sense of where the shapes and intervals you are looking for can be found.
I also find it is a good memory aid when learning a song as it encourages you to learn how the song sounds rather than just which frets to play. It's a small distinction but an important one.
Because when you singing solo while playing it, this makes your soloing not just a running-down-scale solo, but something more interesting than that. You have theme melody or combination of notes which makes sense to play! or anyway answer is: for extending your imagination!
The human voice is probably the most interesting musical instrument there is. To be able to articulate vocal sounds (ie words) as well as notes is something only a few instruments can mimic (guitar, trumpet, sax come to mind).
With guitar then, vocalised notes - ie. notes that you are singing/humming, will have vocal articulations that sound much more interesting than musical scale type soloing. A good old B.B. King Blues lick is instantly recognisable and hummable.
This is why Blues solos are always popular - the bends, slides, hammer-ons, pull-offs that we can consider soloing techniques - when combined together, do go a long way to mimicing the sound of person singing. It's emotive. It reaches out and connects.
Arguably, scalar music can still be interesting (Joe Satriani comes to mind instantly) but the responsibility is on the player to retain some musicality to it instead of it sounding like some exercise - or worse still - just gibberish that you can't hum either way.
So if you learn to sing/hum the notes that you want to hear - your playing should improve on a level that is more attuned with the human characteristic. Your slides and bends will sound more "melodic" or personal/human simply because you are articulating your notes the way you would sing.
It helps you write better songs/melodies because people can always relate back to a human voice (eg. while we're on the subject, can you hum "Surfing with the Alien" to yourself? I bet you can - even the wild fast parts). Or you can construct better melodies with/without scalar runs because you can hear how your voice sounds behind or in front of it.
It's all music at the end of the day - and if you have 2 instruments to play with to create great music, why not?