When I get asked this question, I break it down like this (and I'll credit Bryan Peterson's "Understanding Exposure" book for this logic)...
The aperture of a camera lens is measured in f-stops - the smaller the f-stop number, the *larger" the opening for light to pass through.
That was the confusing part for me...
So, if the sensor of a camera needs a certain number of units of light in order to create/expose a photo, then a lens with a larger opening (the f/1.8 above) can let in more units of light per unit of time to develop a picture than the f/4.6 lens.
Take it a step further and consider ISO, which is the sensitivity of the camera's sensor to light. The higher the ISO, the more sensitive to light the sensor will be to that incoming light, but a higher ISO can also result in more pixel noise (aka picture graininess).
What a slow lens typically means to the people I talk to is that that they will likely be very unhappy trying to snap their indoor sports photos because their slow lens cannot let in enough light to allow for a faster shutter speed (to stop action) and lower ISO (to minimize noise).