If you think of the lens like a hose, light as water, and the "perfect" exposure as a bucket. The question is how long does it take to fill the bucket to get that "perfect" exposure. If the water (light) is flowing at a constant speed, the you can fill the bucket "faster" by getting a bigger hose.
SO, the lens maximum f/stop number is how "big" of a hose the lens is. Things are a little reversed so stay with me here. The smaller the f/stop number is, the LARGER the aperture opening is. So this means an f/1.2 is a LARGER aperture than an f/22.
With this in mind, if a lens is called a 50mm f/1.8, then it will be a wider "hose" (aperture) than a 50mm f/3.5. Lenses are typically identified by their focal length (50mm in this example) and their maximum aperture (f/1.8 and f/3.5 in this example).
Therefore, the 50mm f/1.8 is "faster" lens than the 50mm f/3.5 because it lets more light through meaning that you can leave the "water" running for less time. Basically, you can use a faster shutter speed to get the same amount of light if the lens is set at its maximum aperture.
Does this analogy make sense or did I completely throw a handful of dirt in the bucket making the water muddier?