Socially awkward Sims could have awkward results from socializing with others. This affects even two Sims who are best friends or even romantic partners with each other at the highest levels of positive relationship.
Socially awkward Sims may miss opportune moments and mess up punchlines to jokes.
Socially awkward Sims learn Science skill at 15% faster rate.
Socially awkward trait does not affect every social interaction, least of all those added by other expansion packs. It usually affects more general interactions like "Chat", "Get to Know", "Argue", "Insult" (Teen insults don't seem to be affected) and "Flirt". However, more specialized socials like "Ask About Day" and "Tell Funny Story" can also be affected.