This is an often raised question, so I will just copy an older response I once made:
Good question and hard to answer in an easy way, but one definition is that shyness is confidence related where as introversion is a question of energy. For example does Bruce Springsteen, Julia Roberts or Warren Buffet come across as shy? I think, normally you wouldn't say so, but they are introverts who manage to project a confident public persona. So to provide an example explaining the difference between introversion and shyness, imagine you have a shy person as well as an introvert who need to ask a librarian for help. Both will hesitate, the shy person is hesitant because he/she might think that the librarian is going to think he looks or acts funny, the introvert is hesitant because of the energy he/she will deplete in having to spend to initiate and complete the transaction(introversion in a nutshell has a great deal to do with not only how you get your energy/ - andperhaps more tellingly, how to preserve it).
So, if you interact with introverts, you will over time notice that an introvert tries very hard consciously and subconsciously to preserve energy(eg. refrain from getting tired). An interesting fact of this is that an introvert's energy is often being drained even when he or she does things that he finds enjoyable, eg. like going to the movies - which is why introverts need a lot more downtime in order to recover after an activity, as opposed to an extrovert who in no time is ready to go out again(sometimes several times a day(always been a mystery to me). To come back to shyness and how this relates to introversion, another example is if you engage in some kind of social activity say like a lunch with relative strangers, for example a business lunch. A shy person feels akward because he might think that the people will think he is strange or that he has nothing interesting to say, whereas an introvert can very easily be very much at ease at such a function and appear very confident and extroverted, but after say 2 hours he will have to escape in order to get some downtime, because the experience for him after a prolonged social exposure is similar to that of a battery being depleted (opposite to an extrovert whose batteries are being charged). I recall being at a party about a half year ago, I was managing quite well and particpated in many conversations(eg. in short, not shy at all), but after some hours of this constant social exposure I wanted to escape to get some downtime, my bad luck was that I had no refuge to go to, everywhere I went there were people who then wanted to entertain me,(well intentioned, because they wanted to ensure I had a good time) - and I remember that was really draining for me. Another way to llustrate the difference is that when a shy person is engaged in social encounters he will appear lacking in confidence, whereas an introvert on the other hand often comes across as haughty(because she is in lack of a better word, bored with the whole concept of social chit chat), this often gives the false image that introverts are a bit coldhearted and not interested in other people(which if you asked the introvert would most often result in an instant and indignant denial). However, and this is why there probably is so much confusion and mixing together of the two, introverts can very easily be shy too and often are, however technically speaking the two things are not the same, you can not combine them in to one concept by assuming that when somebody is introverted that is the same as being shy, however it is possible(and not uncommon) to be be both introverted and shy, as it is possible(and not uncommon either) to be extroverted and shy at the same time. In short introversion/extroversion is about energy, shyness about confidence.
OK, hope this helps.