The weight of an oil represents its viscosity, which is a description of the thickness of the oil. Viscosity is typically measured as the standard time it takes the fluid to run through a standard size orifice at a specific temperature, usually 40 degrees or 100 degrees Celsius.
The lower the weight number of the oil indicates a lower oil viscosity, but the weight rating is meaningless unless it is referenced at a specific temperature. Some oils have multiple weights listed, such as 10W-30 that describe its thickness in relation to its temperature. The first number represents the oil's viscosity as measured by centistrokes when cold, and the second number represents the maximum viscosity to which it thins when hot.
At cold temperatures the polymers in an oil are coiled up and allow it to flow at the low indicated rate. As the oil begins to warm, the polymers begin to uncoil. They develop into log chains that inhibit the oil from thinning as much as it would.
The Society of Automotive Engineers developed weight standards in the 1920s. At that time, a driver had to change the weight of the motor oil in his vehicle to match the changing seasonal temperatures. Over time improved additives were developed to create modern all-season oils.