A baffle is anything that 'blocks' the current of your filter. The most common way to make a baffle is to take a water bottle, cut both ends off it then cut it open and stick it on the outflow of a HOB filter. People have also had success siliconing a sponge over the outflow or placing a plant in front of it.
The 'cycle' is the nitrogen cycle. It is basically a process where bacteria break down waste molecules into a less harmful compound. Explained:
Rotting food and fish waste produces a toxin called ammonia. This is usually what kills fish when the tank isn't cleaned often enough. Given enough ammonia, bacteria called Nitrosomonas start living off it and starting a colony in the tank. They live on all the surfaces, primarily the filter because it contains the most surface area. They eat the ammonia and produce a more-harmful waste product called nitrIte.
When nitrIte builds up, it attracts another kind of bug called Nitrobacter bacteria. They do all the same stuff as Nitrosomonas, only with the nitrIte instead of ammonia. What comes out the other end is a chemical called nitrAte. It's only harmless in big amounts. You then vacuum the nitrAte out of the tank when you do the water change. It doesn't take alot of vacuuming to remove.
In an uncycled tank, you skip the bacteria by sucking all the ammonia up yourself. Since you are cleaning out all the ammonia before the bacteria get a chance to dig in, they never really colonise the tank. So you take care of all the ammonia yourself, which requires bigger water changes to eliminate.
AMMONIA >nitrosomonas bacteria> NITRITE >nitrobacter bacteria> NITRATE => Water Change