Inner hearing is, IMHO, probably the most important thing for a musician to develop.
As others have said, far too many people learn to play an instrument by associating the note they see on the page with 'where to put my fingers' and don't HEAR what they are doing. I know - I was one of these people...
Kodaly felt that a good musician should be able to 'see what you hear and hear what you see'. In other words, you should be able to hear in your mind what the music will sound like BEFORE you play it. As jazzywench said, this skill can be likened to the ability to read words in your head. Imagine if you could only ever read a book by having to feed the code of the letters into a machine which would then produce the sounds of the words for you! - But this is exactly how many people learn to 'read' music.
The majority of children in Hungary will have reached the stage of being able to sight-sing a simple pentatonic melody before they lay their hands on an instrument, and they naturally sing before they play.
Kodaly also said that he felt the four aspects of being a good musician were to have a well-trained ear, a well-trained mind, a well-trained heart and well-trained fingers - and that if any one of these raced ahead of the others then problems would ensue. In my experience, we tend to train the fingers before anything else...which is why so many people have problems with rhythm reading, aural work and so on.
Singing is the best way to activate the inner hearing. So - yes, sing before you play if you possibly can! If not, play then sing then play again - and you will find that the quality of your playing will have improved after you have sung the line or phrase. This will help also to produce the 'perfect sound' in your head that Steve talks of.
Good luck and let us know how you get on. If I can be of any more help please just PM me. A Kodaly course could really help so if you let me know what part of the country you're in I may be able to help here.
Best of luck!