The Brief: Thirsty means "eager."
Thirsty typically has a sexual connotation, as in someone who is eager for sex. This could mean they are trying to be seen by others as sexy, or they are actively seeking others in a sexual way. Thirst is often associated with desperation.
Photos posted online meant to illicit attention in this way are called thirst traps.
I’m buying Resident Evil 2 just so I can thirst over Leon pic.twitter.com/KjaMOS3alH
— Mia (@itsmammamia) January 28, 2019