Yes the boiling of water does get rid of and kill any parasites that can be in the water.
Boiling water is a natural effective way of disinfecting water for drinking purposes and kills any disease causing organisms, including viruses, bacteria and yes the parasites.
Boiling the water can also change the taste of the water and make the water taste flat but you can get rid of the flat taste by pouring it out of the container you boiled it in and then pouring it into another container and letting it sit for awhile before drinking it.
You can also add a pinch of salt to the water after boiling it to make it taste better.
So if you're out camping or need some emergency water to drink you can boil it if possible to kill off the bacteria, organisms and parasites and it will be safe to drink.