PurpleAngel's posts may be unnecessarily confusing.
A sound card contains a DAC, but a DAC is not necessarily a sound card. Traditionally, "DAC" refers to a micro-chip that converts digital signals to analog. Only recently has it been common to use the term to refer to an entire physical product that has digital inputs and analog outputs. The micro-chip concept is more accurate though and DACs should be thought of that way, not as physical products.
Modern sound cards have 3 important parts: a DAC (Digital to Analog), an ADC (Analog to Digital), and a DSP (digital signal processor).
The chain of events in a computer start in software, where an audio signal is digitally created (or stored) in a binary format (common formats include WAV, MP3, FLAC, etc). The audio signal is then passed over to a sound card, where it goes through the DSP first for any effects to be applied (if applicable, as all DSP settings can be turned off in software) and then it goes to the DAC, after which it's sent, in analog form, to a pair of speakers or headphones.
Sound cards don't have "amplifiers" in the conventional sense. The native output for sound cards is referred to as "line level" which is amplified outside of the computer, usually by the speakers that are plugged in. (Though there are exceptions, as speakers are available in active and passive versions - passive speakers don't have internal amplification.) Some sound cards have headphone jacks, in which case they do have small "amps" to drive headphones directly.
http://computer.howstuffworks.com/sound-card.htm
http://en.wikipedia.org/wiki/Sound_card
http://en.wikipedia.org/wiki/Audio_signal_processing