A fangasm is (aside from being a fan-made portmanteau of 'fan' and 'orgasm') an emotional or mental climax experienced by a fan of a work.
At its mildest, the fangasm can have an average fan experiencing genuine happiness, a slightly quickened heartbeat, and the irresistible urge to smile like a loon for the rest of the hour. At its strongest, the fangasm can have the afflicted actually moving around in a sudden burst of energy, babbling nonsensically about how 'oh my God, this is going to be so cool!'. Female sufferers of a fangasm are particularly prone to squeeing, though males have also been known to squee.
While the specific reasons for a fangasm may differ from fan to fan, the two most common triggers are:
1. The afflicted fan hearing news about the status of a work or the creator of the work (such as a beloved author promising a sequel, an actor announcing his involvement in a highly anticipated movie, the adaption of a work to a different form of media by people who actually like the original work and/or have a good track record for media transitions, the announcement that a favorite band will be playing in a place nearby, etc.)
2. Something within the confines of the work itself. (Such as a well executed plot twist, a dramatic reveal by one of the characters, a clever idea done well, a character doing something just generally awesome that has a long time fan internally whooping in joy, etc.)
The type of media and/or genre of the work in question doesn't matter, as fandom knows no boundaries.
Important note: despite the name, the fangasm itself is nonsexual in nature.
However, the reason for a fangasm may be rooted in something sexual (such as someone fangasming over the fact that a sexually attractive actor/actress they like is taking a role in a television series they like).
Also known as a nerdgasm.