Update 2023: some of the elements of my answer below assume a DSLR, and in some cases mirrorless system make some of these issues less of a challenge. The points about zoom lenses requiring a more complex design are all still valid

A prime lens has a much simpler design, so for the same price, and weight, you can get larger lens elements and therefore a higher aperture.

However, there are some other factors to what you're asking. In the case of a 18-55 zoom lens, the lens has to have a retrofocal design, because at the wide end you are going down to much smaller effective focal length (18mm) than the physical distance between the lens and the sensor would otherwise allow. A retrofocal design means that many more lens elements are needed; it essentially is like combining a simple lens with a telephoto lens in reverse. A more complex lens has more elements, and to fit these into the available space they need to be certain sizes relative to each other, severely limiting the maximum aperture.

Now, a zoom lens uses the same lens elements throughout the zoom range: it does not "swap in" different elements depending on where you are in the zoom range. So a zoom lens that goes down to a wide angle (such as 18mm) must use the same number of lens elements even at the telephoto end, and throughout the zoom range.

Therefore, the limitation of maximum aperture imposed by the complex retrofocal design to permit wide-angle photography persists throughout the zoom range.

Additionally, remember that aperture is quoted relative to the focal length f, so getting a higher aperture number is harder as the focal length increases, which is why on a zoom lens you never see the aperture number improve as you zoom towards the telephoto, it always degrades (or is constant). That is, a zoom lens may be f/3.5-f/5.5 from wide to tele, but the numbers would never go in the opposite direction.