A fixed blade knife is permanently open, there are no moving parts in the fixed blade knife, so its considered strong and reliable. There downside, however is the knife is always open, you have to carry it in a sheath and wear it which can be bulky.
The folding knife has a blade that folds back into the handle, it also has a locking feature that prevents the blade from closing while in use, so the knife is more compact and can be carried discretely. But this design is also the folding knife's biggest drawback, as the hollow handle and pivot point where the blade folds are weak points compared to a fixed blade knife, although the use of high quality materials such as titanium can reduce this risk.
Generally speaking if you are say hunting or fishing you dont want to be messing about opening a folding knife with dirty or wet hands so a fixed blade would be the choice, whereas the every day carry such as a carpenter will use occasionally and want a smaller more easily carried blade so a folding pocket knife would suit in this situation.