There's a nerve running along the fleshy part of your palm and is affected from too much pressure on it. It's a common malady with tourers or anyone riding more than an hour sometimes. The best way to combat the problem is too change hand positions often. If you have straight bars get some bar ends or even drop bars. Additionally, try keeping some of your body weight off of your hands when riding. Some folks like gel-padded gloves.

There's alot of info on this site regarding hand numbness. Try the search function on this site to get more info from more knowledgeable folks than I.

Cheers.