Explain how the battery in this works and how its all connected. Motor as well please. Prismatic Cell battery

It's a Lithium Ion Battery according to the speaker.  That would appear to be a mixed blessing.  The LIB has lower weight and carries a greater charge, but one of the advantages of Lead-Acid batteries is the greater weight -- it provides a lower center of gravity.

See http://www.youtube.com/watch?v=3IVj44t49T4

What is the PHP component of your question?

@kode99: +1 for a really good answer!

@kode99: Thank you very much, helpful indeed. I'm working on building a wheelchair of my own. I also found it funny when he got out of the chair and lifted it over the curb.

Check this out for a really fun hub motor use,

http://www.youtube.com/watch?v=USTOxlv_7m0

Aside from the very cool bike his use of recycled rechargeable is interesting.  

Also check out Golden Motors,
http://www.goldenmotor.com/

and go the to the e-wheelchair link.

Looks like the same wheelchair from your video with some modifications.  They also have the controller as a separate part as well as a variety of hub motor wheels for different applications.  Some of the designs for cycling may offer some nice alternatives for wheelchair applications.

Here's how simple a electric conversion for a standard wheelchair can be,

http://www.youtube.com/watch?v=6P1C-GdOohs

Not sure how to get my hands on