Why would the water drain from the tank but not flush or suck the water down through the toilet bowl when you flush?
Do the rest of the fixtures in the bathroom drain well? If they
do not drain well, my guess would be the venting of the plumbing
system. If all of the other fixtures in the bathroom drain well,
then there is probably something in the trapway of the toilet.
Assuming it is just the toilet that is having problems, then a
closet auger might do the trick. Hope it helps.