The amplifier is the heart and soul of your hifi system and is the component responsible for taking a source signal and presenting it to your loudspeakers. Amplifiers typically come in three formats; a power amplifier, a pre-amplifier and an integrated amplifier. The power amplifier, as the name suggests, is the muscle responsible for powering your dedicated loudspeakers, while the pre-amplifier is the brain of the system, featuring inputs for your source components to pass this information, along with volume control, to the power amplifier.
An integrated amplifier features both the power amplification and preamplification elements combined into a single box solution. This offers a high fidelity experience with the convenience of taking up less space than a separate pre/power system, but as with anything hifi - the more separate you can get the boxes, the more they are able to focus on one job alone and perform to a higher standard. In most cases, a pre-power system will outperform an integrated system at a similar price point.
In addition to these formats of traditional amplifier, more and more headphone amplification units are being designed and engineered by quality brands as the demand for high-end personal audio increases. A headphone amplifier works much in the same way as an integrated amplifier designed to power speakers but is designed specifically to cater to the impedance levels of a designated pair of headphones.
A 'phono-preamp', also known as a phonostage, is a small component designed to sit between a hifi preamplifier/integrated amplifier and a dedicated turntable. Because the signal that the phono cartridge of a turntable picks up is so quiet, connecting a turntable directly to an amplifier via a line input will mean that you have to turn the volume up extremely high to hear anything from the deck. This will also sound distorted and over work the amplifier. A phono preamp/phonostage will bring the cartridge signal to 'line level' and make it compatible with the integrated amplifier's line inputs. Phonostages come in Moving Magnet and Moving Coil variants, depending on the cartridge being used.