Your source can be anything from an external CD deck, tape deck, external AM/FM tuner, iPod, MP3 player, DVD/Blu-ray player, PS3/Xbox, etc.. Those are your "source" devices where the audio/video signals come from. In your case, this receiver does support AirPlay (using an iPod Touch for example), which is also considered a source.
Your receiver does exactly what it's titled, to "receive" these sources (essentially acts like a hub), and sends the audio/video signals to wherever you designate them. Typically, audio goes out of the receiver to your speakers, and the video would go out of your receiver to your TV.
Bi-amping in its simplest terms means "two amps" .. That being said, what it does is "dedicate" a certain amount of power (in the form of watts), sending power to your low-ends or "woofers", and a separate dedicated amount of power, sending power to your high-ends or "tweeters."
Eg. Source Signal >> Receiver >> Speakers (with internal crossover) >> signal gets split into 2 separate paths inside the speaker, low-fi (woofers) and hi-fi (tweeters)
Alternatively, in your case, each input on the speakers would be coming from a separate output on the receiver, in turn having a dedicated amplifier powering each side of the speaker.
Page 16 of your user's manual explains how to setup your front speakers in a bi-amped setup. In this instance, you use one each of the front and surround back goes to each of the left and right speakers.
Any decent speakers that can use bi-amping will have an internal cross-over and two sets of input terminals. You're basically using one terminal with its own amp to power the hi-end of things, and another terminal and separate amp to power the low-end of things. Keep in mind that when using a bi-amped setup with your receiver, surround sound options are not available.
A cross-over basically works by splitting the signal at what's called a "centred frequency," and anything below that within a certain range (eg. 45hz -80hz, 80hz being the "centred frequency") will get sent to the woofers, and anything above 80hz, to say 22khz, will get sent to the tweeters.
Here's a good article on bi-amping that makes it simple to understand:
http://www.gcaudio.com/resources/howtos/biamping.html
Hope this helps, and good luck!