An amplifier-- often referred to as an amp-- is an important piece of equipment in a hi-fi system, whether you're using headphones or speakers. An amp is the second piece of equipment in between your music and your ears, after a Digital to Analog converter (or, DAC). An amp increases the power of an audio signal to a level that your speakers can use to generate sound.
What exactly is a DAC/amp combo, and should I get a DAC/amp combo or separate devices?
A DAC is a digital to analog converter, a device that converts your digital audio signal into an analog audio waveform that can be sent to an amplifier, speaker, or headphone. Your computer downloads, stores, and streams music in digital format: a stream of 1s and 0s. However, sound is composed of analog waves, and so the DAC converts your music or audio into this form.
A quality DAC by itself is an important part of a hi-fi audio setup. It allows you to decode high resolution music files, even higher resolution than your computer or phone's built-in DAC can support, and convert it into a clean analog signal.