Convention
A convention, or con, is an event held at large scale properties and establishments to gather people with common interests. In the context of chans and the internet, they usually mean anime conventions and/or tech/internet conventions.
Depending on your situation, and your experience, conventions are kickass places to make friends, not feel forever alone, and party all night pissass drunk, or are places where the worst representatives of your hobby tend to congregate at and act like complete fucking dumbasses.
Due to how chans are related to Japanese culture, and so is anime, in Japanese popular cultural nomenclature, conventions usually means these:
Anime Conventions
These places are either kick fucking ass, or you are an arrogant anti social pussyfoot faggot with no skills to even say a simple "Hi!". Depending on where you go, it is exciting as hell or are boring as fuck because of one simple factor: The staff behind it all, or you, essentially. There may also be loads of drama waiting if you are an asshole and/or douchebag, so behave or fuck off (and rightfully so).
Beware of top notch holy shit weeaboos, ranging from teenyboppers who are out of their minds (increasingly rare these days) to shithead smug ghosting (sneaking, nonpaying) assholes who are complete losers outside of their forums where they reign king.
Remember to BATHE. No one gives a fuck if you will come in for a day, but gods man, everyone will if you don't fucking bathe. If the place is open air, your ass is lucky, but good luck meeting anyone a foot close to you either way.
A lot of people here usually cosplay.
In reality, no one really gives a fuck about furries unless you are willing to cause drama over it, furry or not furry. Either way, either preference, you are getting kicked out if you start drama.
If you cosplay as Anon, NO WORDS. It's better that way. Make sure no one knows who the hell you are. If you talk about 4chan openly, if you brag about Anon, if you gloat about your trolling exploits, if you host a panel on it, if you talk like a /b/ board, then you are, officially, a grade A+ faggot. No one likes /b/tards or chan goers outside of their natural habitat.
No one likes oldfags, no one likes normalfags, and no one likes drama. Also, no one likes people who talk like complete faggots fresh out off of the internet who can't speak what's on their mind and can only speak it through an imageboard. Learn to reality or stay home.
Otakon
Otakon is a well known convention in the USA, being held in Baltimore, Maryland. The name of the convention is made up of the words otaku and convention, and is the longest running of any anime convention in the US. The convention was primarily focused on fanatics of the Japanese anime subculture, though it has expanded to selling mainstream American media.