Objective lens diameter is the diameter of the objective or front lens measured in millimeters (mm). This figure is generally shown at the second figure in a scope configuration. For example, a 4X32 scope has a magnification power of 4 and a 32mm diameter objective lens. A 6X42 has a 42mm diameter objective lens.
The lines in the image above depict the objective lens diameter and how it's measured. Objective lens diameter is also considered a measure of the amount of light that can enter a scope. Objective lens generally range anywhere from 32mm all the way up to 75mm. The larger the objective lens, the more light than can enter the scope.
Notice the amount of light in the 50mm compared to the 32mm? Please understand that larger objective lens will only transmit more light when they are set on their highest power. So if you took a 6X42 scope and a 8X50 scope made by the same manufacturer, the 50mm model is only going to pull more light than the 42mm when the 50mm is set above six power.
Keep in mind that the higher you go in objective lens diameter, the larger the lens will be in size and heavier it will weigh. Also realize that some of objective lens that exceed 48mm or so may require special rings and bases for mounting as they will have to mounted higher off the rifle. This higher mounting can impact eye relief and result in a less than comfortable position during shooting. For most applications, 38mm to 48mm will work just fine. I've got a scope with a 50mm lens and it's only used for long range shooting.