Integrated amplifiers pack both pre- and power amplification into one box, and all of the stereo amps on this list are this type. The advantage is neatness due to fewer boxes and cables and the fact that the pre and power stages will have been tuned to work optimally together.
Alternatively, you can buy individual preamplifiers (which essentially handle input selection and volume control) and power amplifiers (which increases the amplitude of the audio signal) and these have advantages, mainly in that they keep the sensitive preamp circuitry away from the electrically noisy high-current power amplifier section, and having separate power supplies helps improve sound quality too. It generally makes sense to pick a pre and power pairing from the same manufacturer as they will have been tuned together.
More information can be found in our how to choose and set up a stereo amplifier article.