The viscosity will determine how easily the
oil is pumped to the working components, how easily it will pass through the filter, and how quickly it will drain back to the engine. The lower the viscosity the easier all this will happen. That is why cold starts are so critical to an engine because the
oil is cold, and so relatively thick.
The lower the viscosity, the less the load the
oil can support at the bearing on the crankshaft. The higher the viscosity, the better the load it can support. There is a trade-off, since the higher the viscosity, the more the drag at the bearing, and hence, potential power loss, or increased fuel consumption. So a compromise is chosen to minimize power loss, but maximize load support.
Until the 1960s it was quite common to change the oil depending on the season with oils as low as SAE 5W for very cold ambient conditions and SAE 30 and 40 grades would be typical for Summer use, and sometimes a SAE 50 grade would be substituted if the engine started to use more oil. Multi-grade oils were developed to allow year round use as a result of artificially raising the VI (viscosity index) of the oil.
Scientists discovered the use of polymers and the fact that these would expand with heat. VI Improvers are polymer material that expands as the oil warms up. This does NOT thicken the oil as is often stated. It merely slows down the rate at which oil thins out as the temperature rises. The base oil in use in a multi-grade (aka multi-seasonal) is the first number (such as 10W or 20W), whereas the second grade is the viscosity achieved using the VI Improver (such as 40 or 50). 20W50 is a base oil of SAE 20W and the viscosity grade at running temperature is SAE 50.