Welcome to WS tigercub
A preamp takes the small signal (1 to 2volts normally) from your source (CD Player, DVD player, output from MP3 player, laptop, phone, etc) via it's line stage and sends it to the power amplifier.
The power amplifier turns that small signal into a more powerful one and that in turn drives the coils inside your speaker. Together with the permanent magnet that makes the cones move.
A receiver has a preamp and amps built into one unit with the bonus of having a tuner. Receiver is short for radio receiver.
An integrated amp is a preamp or passive volume control and amps in one box without a tuner.
A full function preamp includes a phono stage along with the line stage.
A DAC is a Digital to Analog Converter. Pretty much every digital device has one built in. Some devices have digital outputs (Orange RCA) is SPDIF and the square output is called TOSLINK. These can be found in older CD players and DVD players and Cable set top boxes. Computers will typically allow you to output digital via USB. Using the digital outputs allow you to use a DAC of your choosing instead of the ones built in which are usually of lower quality in construction and performance. Strictly speaking you don't need a DAC but it is a route for improvement. Be careful not to send a DTS or Dolby Digital Signal to an audio DAC as this may cause damage.
Your iPad can be connected to the preamp, integrated amp or receiver with a mini phono to RCA cable via it's headphone jack. Some new receivers are equipped with Apple Airplay and will take streaming music from your iPad. If the receiver you choose doesn't have Airplay you can use an Apple TV and connect it either via analog outputs (mini phono to RCA) or via mini toslink to toslink if the receiver has a digital toslink input. You can also send this to a DAC with toslink in and send the analog output of that to one of the pre/integrated or receiver's analog input pairs.
Hope this helps and once again, Welcome to WS