Oftentimes, CTR and conversion rate have an inverse relationship, so what you're seeing is quite common.
Beware that the very optimizations that you employ to increase conversion could very well end up suppressing your CTR... There are many great threads on this forum regarding increasing conversions - I'd start there.
1. relevant topic - your keywords and ads might be getting them to click but are they finding what they are looking for
2. I search "stock" - you search "stock" - I could be looking for the next hot IPO, you could be looking for recipe for chicken stock, or stocking - just because I have a lower CTR doesn't mean that my ads and product are irrelevant - I could have a sparkling conversion - because the people who are clicking are getting what they want.
Points to CTR and conversions being inverse.
Target and specific keywords also vary CTR - Ad content, flow - blah blah blah.......
So many things effect these numbers it hard to pin it down to a simple list. Could be you have a phone number in your ads - people aren't clicking but they are calling?
Its Friday and I'm babbling.
Have a good weekend
M