Stresszyme is a product that contains bacteria that consumes mulm and detritus. The stuff that can build up in hoses and on your filter media. As far as im aware it isnt something that grows like the beneficial bacteria responsible for your cycle so you need to add it to your tank periodically. At least it says on the bottle you need to keep adding it. The detritus ordinarily would break down and produce ammonia, so the product says it will help your cycle because it reduces the ammonia produced by your aquarium.
Do you need it? No. The majority of people manage tanks just fine without stresszyme or similar (other brands are also available). A healthy tank with an established cycle and proper maintenance can manage just fine. In fact a lot of the beneficial bacteria responsible for your cycle lives in the mulm build up because its a ready supply of food.
Personally i think its an expense you dont need.