A prime lens is a lens that has a single focal length, as opposed to a lens which can vary its focal length, known as a zoom lens. Common maximum apertures found in modern prime lenses include f/1.2, f/1.4, f/1.8, f/2.0, and f/2.8. Common focal lengths for prime lens designs include 24mm, 35mm, 50mm, 85mm, and many others. While the inability to zoom in or out may be considered a disadvantage with a prime lens, many photographers use prime lenses for a variety of reasons, from boosting creativity to portability and affordability.
Prime Lenses Explained
Prime lenses, thanks to the simplicity of their design, often provide a faster aperture than zoom lenses. Primes are often smaller and lighter than zooms as well, making them more portable and inconspicuous. However a very "fast" (and sharp) prime can easily be bigger and heavier than a "slow" (and sharp) zoom lens.
A History of Prime and Zoom lenses
Historically, zoom lenses are a relatively recent invention; early camera optics were entirely single focal length designs. As zoom lenses became more common, they were often a serious compromise of image quality compared to a prime lens: prime lenses were both sharper, and faster-aperture.
With the advent of computer-aided design, however, zoom lenses began offering both features: professional-grade sharpness, and relatively fast apertures. While prime lenses are still capable of the fastest apertures such as f/0.95, or f/1.4, many (sharp) zooms exist with an f/2.8 aperture, and some even with an f/1.8 or f/2 aperture.
The advantages of a prime lens
Despite the improvements seen in modern zoom lenses, prime lenses can still offer a myriad of attractive features. Prime lenses can be smaller, lighter, and more affordable than zooms. While having a prime lens that is all three of those things is common, faster apertures are another separate advantage of primes, one which sometimes requires a compromise on weight or affordability.
With this in mind, different photographers choose different prime lenses for different reasons.
Fun fact about prime lenses: While many prime lens' focal lengths are indeed not prime numbers, (24mm, 50mm) ...there are a few lens manufacturers which seem to frequently use actual prime numbers when designing their focal lengths. For example, 31mm and 43mm, which are Pentax "Limited" lenses.