Opening up the lens refers to adjusting the aperture, and therefore the lens opening, to a wider-diameter aperture. For example, going from f/11 to f/5.6 is opening up.
Opening up refers to decreasing or using a smaller f-stop number, which increases the amount of light entering the lens. As a photographer you could say, “I opened up from f/11 to f/5.6.”
Opening up the lens adjusts the lens to a larger diameter. Think of opening up and increasing the size of the lens opening to let in more light. In other words, think “open up and let the light in.” This may help you from becoming confused with opening up actually being created by using a smaller number aperture.