Music theory is very important if you want to improve as a musician. Imagine if you wanted to be a car mechanic and you only knew how to fill up the water for the window wipers, you wouldn't get very far! It is only possible to go so far as a musician without knowing at least some music theory.
Old style music theory can be a bit boring and include stuff you really don't need to know, that is why a more modern approach to music theory can be practiced with a good private music teacher. It's more fun, more logical and more practiced based.
Depending on your instrument of choice, music breaks into three basic areas:
Melody
Harmony
Rhythm
Melody - is the part of a song which can be whistled or hummed. This relates many to knowing your keys and scales.
Harmony - could be explained as the background of the song, out with the melody. In a band, this is usually performed by the guitarist and/or keyboard player.
Rhythm - The feel of the song, the whole band contributes to the rhythm, however, usually the drummer and bass player are the people who hold the 'groove'.
Books such as 'Contemporary Music Theory' by Mark Harrison or the 'AB Guide to Music Theory' by Professor Eric Taylor are a good start, but you really will save a lot of time and effort with a good teacher to assist you. Check that your teacher has a degree in music or equivalent.