Adam has provided a succint answer to your question.  However,  you should read the relevant chapters in David Metzler's 'Biochemistry:  The Chemical Reactions of Living Cells'  which is the still the best text on cofactors/coenzymes I know of. I have taught enzyme chemistry for ten years and this still the best textbook. OK

Cofactors are prosthetic groups that are either covalently or noncovalently attached to the enzyme and participate in its catalytic function. Without the cofactor, the enzyme will almost certainly be inactive.

Adam has provided a succint answer to your question.  However,  you should read the relevant chapters in David Metzler's 'Biochemistry:  The Chemical Reactions of Living Cells'  which is the still the best text on cofactors/coenzymes I know of. I have taught enzyme chemistry for ten years and this still the best textbook. OK

Adam and Robert are right. I agree with Robert about Metzler`s textbook.  To go further, perhaps you ask for the difference between bound and free cofactors, Some of them are usually free and they are bound to the enzyme only during the catalysis (as most of NADH-dependent dehydrogenases), whereas other cofactors are bound to the enzyme even without catalysis (such as most of the FAD-dependent dehydrogenases).

maybe it is some enzyme that needs  no cofactor.

enzyme catalyse the reaction without need of the Co-enzyme like hydrolytic enzymes lipases, proteinases etc these are called Co-enzyme free enzymes

Some enzymes require NADH/NADPH or metals as enzymes to catalyse the reaction  

Let's get this straight - to my knowledge there is only a small proportion of enzymes which don't require organic cofactors. Examples are proteases, lipases and even Diels-Alderases (although many require metal ions - or metal clusters). Even if one doesn't count  metal ions as co-factorial, less than 15% of known enzymes do not function without an organic cofactor.  However for a lot of these - particularly ATP/GTP ( NOTE the distinction between the terms synthetase and synthase!), and NAD/NADP requiring enzymes the cofactor can be realistically viewed as a substrate (since it is not recycled withinin the enzyme complex - although there are a few exceptions - for example the NADP in certain carbohydrate rearrangement enzymes is very tightly bound) .  FAD/ FMN are tightly bound (FMN is actually covalently attached in a few bacterial enzymes). Biotin & lipoate are covalently linked to their carrier proteins. PLP-dependent enzymes have an active site lysine to which the PLP is attached as an imine (in recombinant proteins one has to work these up with PLP in the final buffer to regain activity).  The widely accepted definition of a cofactor requiring protein without the cofactor is an apo-protein. Hope this helps....but I really think you should read the relavent chapters in Metzler.