1. Someone who acts as an expert but clearly isn't.
2. Knowingly guessing at a response but speaking with conviction. A combination of Faux (fake) and SME (subject-matter-expert) (Pronunciation: \ˈfō-smē\). It can be used as an adjective or a verb.
You: "I wonder how long it took to build this roller coaster?"
Fauxsme: "I bet it took 40 guys at least 3 months to finish this off."
You: "Don't be a fauxsme, you clearly have no idea whatsoever."
Or
If I had to fauxsme this one, I'd bet it took 40 guys at least 4 months to finish this off.
Regarding one's own behavior or oneself as "awesome" when in fact the behavior is misguided, or embarrassing, or one is really living a thinly-veiled life of mediocrity and fear.
The hipster was convinced that he was completely awesome, but those around him knew he was fauxsome, with no real ideas or action to back him up.
Rog bragged to everyone about how he was going to jump out of the plane, but he pissed his pants and chickened out at the last minute. He was so fauxsome.
Nickname given to bales of marijuana thrown overboard or out of airplanes. Origin is reportedly from members of the US Coast Guard in the area of Southern Florida.