During pregnancy, some women feel palm pain during pregnancy. This is simply a sensation caused by carpal tunnel syndrome. The Carpal tunnel is a connecting tube through which the nerves in the hands and fingers run through.
During this time, this tube tends to swell due to an accumulation of fluid in the spaces between the tissues, which in turn compress the nerves. The pressure applied on the nerve caused due to the swollen carpal tissue causes pain in the main nerve and the other smaller nerves which then shifts to the thumb and fingers.