A preamplifier, or preamp, amplifies a microphone's signal from mic level (typically -60 to -40 dBu) to line level (typically +4 dBu), an amplification of around 60 dB. Without this amplification, the microphone's signal would be too weak for an analog-to-digital converter to capture accurately.
Every audio interface includes at least one preamp. The quality of the preamp determines how much clean gain is available and how much noise is introduced at high gain settings. A good preamp adds significant gain with minimal noise; a poor preamp becomes audibly hissy when pushed.
Some microphones require far more gain than others. The Shure SM7B, a popular broadcast dynamic, needs around 60 dB of clean gain to reach a good recording level — more than many entry-level interfaces can provide cleanly. In these cases, an inline preamp (like the Cloudlifter) adds 25 dB of clean gain before the interface.
Standalone external preamps (hardware boxes separate from an interface) are used in professional and high-end home studios to add character and color to recordings. Vintage-style tube preamps add warmth; transformer-balanced designs add presence and depth. For most home studio applications, the built-in preamps in modern Focusrite, PreSonus, and Universal Audio interfaces are transparent and excellent.