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My website ranks at the top for a keyword that i had not placed a bid for. I did bid for keywords like website designers, website designs etc.
However, my website shows up for the keyword web designers. Does Google Adwords ranks my pages for keywords synonymous with the keywords i am bidding for ?
Read up on match types in the help files, and also on the Search Query report.
[...] Does Google Adwords ranks my pages for keywords synonymous with the keywords i am bidding for ?
Yes, if you use broad match
I would actually answer this in a slightly different way, by saying that it might show for such keywords - and that if there are keywords for which you definitely want to appear, then it's best include those keywords as exact matches.