If you look super close at the music chart, you will notice that the last notes of each part (for example, the low G in the bass part) has a squiggly line attached to it. What is this called, and can someone explain to me what does it mean to do to that note?
Glissandos are usually between two written notes. That score looks like a big band arrangement. The big-band terminology is “falls” for descending pitch and “doits” for ascending. Here's a video of how to play them on trumpet:
They are sometimes drawn as smooth curves, not wiggly lines: http://lilypond.org/doc/v2.18/Documentation/notation/expressive-marks-as-curves#falls-and-doits
I've no idea why the score also shows them on the piano part - that doesn't make any sense.
This is clearly a big band jazz chart, so think about the kinds of sounds you would hear in that kind of music.
Jazz is full of all sorts of bends, blips, doits, falls, etc. A pretty good resource for how these are notated and executed is here:
This is another resource from the same website, taken from the US Army Field Band, it's effectively a technical manual for playing big band music:
In the example you posted, this is a fall played by the entire ensemble at what looks like the end of a shout chorus. The fortissimo, accented whole note on which the fall is notated indicates that the band should probably hold the pitch for a few beats before falling off.