Ships on the ocean have to deal with waves and weather. Stabilizers are what help the ships stay straight and upright, which cuts down on seasickness.

First, people tend to get seasick because of a disconnect between what they see and what their inner ears sense. On land, you can see the ground and sense how you move across the ground. At sea, you lose all visual reference and therefore movements can upset your stomach.

The smoother the sailing, the less likely this problem will occur. Therefore a big ship - which resists waves and weather - is far smoother than a smaller ship. But there still could be movement if there were large waves or a storm. This is where the stabilizers come in.

Stabilizers are in essence like big 'wings' that stick out of the left and right side of the ship, below the waterline. They help keep the ship from swaying to the left or right. The newer the ship, the more advanced the stabilizers are, and the more they are able to keep the ship quite calm even in rough conditions.

If you have problems with seasickness, it's worth it to look for newer ships, with stabilizers, and to take cruises on routes that involve calm oceans.

Note that some cynical people say that cruise ships sometimes deliberately avoid using stabilizers, so that their passengers eat less food :) However, given that cruise ship staff are pressured to get people to drink, gamble, and spend as much as possible on their voyage, I really doubt they'd risk that income by having sick people staying in their cabins!