Oil additive are chemical compounds that serve to improve the performance of base oils. Most motor oils contain additives, regardless of if they are synthetic or petroleum based. The type of additive you choose is based on the job you want the oil to do. For example, a diesel engine would require different additives than the motor of gasoline powered engine in a small car or boat.
There are countless different types of additives for different applications. Every type is essential for providing the proper lubrication and long-term use of motor oil in internal combustion engines. The most important additives for most engines are used for viscosity and lubrication among other things like chemical breakdown. Viscosity can be related simply to thickness, or its ability to flow easily through the engine. If your oil is too thin, it will flow too quickly through the engine, not staying around long enough to do what it has to do. On the other hand though, if the oil is too thick then it will clog up the engine, which you can imagine isn’t a good thing.
There also exist aftermarket oil additives that can serve to further benefit your engine by giving your standard engine oil a little extra kick. There is some controversy surrounding aftermarket additives though, some argue that they only really give the driver a placebo effect, rather than have any significant effect on the engine. As long as your additives come from a reputable source though, putting them in your oil can only benefit and extend the life of your engine.