Since I don't understand it in the first place, I better just give you an example:
Cracked.com example, says otherwise known as "the pettiest hobo crime this side of aggressive panhandling." (WARNING: site graphics could be NSFW, YMMV)
It's not the only time I have seen it but it's the only one I can find via Google Search
The usage that I've seen seems to indicate some sort of comparison. The example above seems to say that "where we live, panhandling is aggressive", but I can't figure out the exact meaning
Note: So far I think I've only seen this phrase in cracked.com itself. Perhaps it's some kind of inside joke, but I certainly don't get it and its usage seems pretty legitimate
EDIT:
Mathias Foster gives 2 other examples: this side of the black stump and this side of the equator.
Best Answer
Cracked.com is a satirical site, and their usage there is, appropriately to Cracked, inappropriate. Aggressive panhandling is very annoying; bilking nations out of tens of millions of dollars in taxes is a little bit worse than petty.
This side of is a common idiom, meaning some (point/amount/quality) up to, but not including another. The Free Dictionary gives this example:
This side of heaven, or this side of the grave are common examples of this idiom, as are This side of (an age).
Dictionary.com gives it's origins in the 1400s, which I was doubtful, until I read this quote by Ben Johnson (1572–1637):