The verb stabilize means to hold steady or make firm. When you climb a ladder, you should stabilize the ladder before you get on it, otherwise you may get a lesson in the laws of gravity — you know, what goes up comes down!
The verb stabilize also means to keep from changing or shifting. If you have a fever and your temperature is all over the place, you can help stabilize it by taking aspirin. The verb stabilize was originally applied to ships and the idea that something like weight or the shape of the ship could be used to produce a steadier, or less wobbly, voyage. Now the verb applies to anything that can be made more steady or stable. You might remember how happy you were when learning to ride a bike that you had training wheels to stabilize you.