The OMEGALUL emote is used when you want to express that something is particularly funny. It shows the distorted, laughing face of the late content creator John "TotalBiscuit" Bain.
What looks like a funny ring at first glance in a quick scrolling Twitch chat is actually the totally distorted face of John "TotalBiscuit" Bain. Like LUL or LULW, OMEGALUL is based on a picture of Bain from 2013.
What does OMEGALUL mean in chat? Basically, you use it when you want to express a very strong laughter, similar to a "ROFL". However, it is also often used as a mocking laugh, for example when a streamer dies in a stupid way and you want to tease him with it.
The OMEGALUL meaning is now known across many other platforms such as Facebook or YouTube. Where the emote cannot be used, people simply fall back on the mere phrase.
But what does OMEGALUL mean? The OMEGALUL emote is a further development of the LUL and LULW emotes. If one assumes that it is supposed to express an even greater reaction than its "predecessors", the addition of "Omega" suggests itself generally stands for something greater, sometimes infinite.
Like so many emotes, OMEGALUL only became really big because of Forsen's community. Forsen's community, which often conspires to "attack" other streamers' chat with emotes, also carried OMEGALUL into many other communities, eventually making it into the Twitch mainstream relatively quickly.
To use OMEGALUL, you have to resort to the common browser extensions, as it is not part of the global Twitch emotes.