We know it intuitively: we trust each person we meet to varying degrees. The trust battery is a metaphor that helps you think about and visualise these trust levels.
The concept is from Tobi Lütke, the CEO of Shopify. He explains, for example, that when a new colleague joins your company the trust battery between the two of you may start out at around 50%. Each time the new colleague acts in a way that earns your trust that level increases, and if they let you down the trust battery level goes down. It can be long and slow to fill up the trust battery yet quick to drain. Each time we interact with someone we are subconsciously considering the level of their trust battery and that level affects how we respond to people.
Lütke says at Shopify they found it a useful way to surface and talk about trust in reviews without it feeling too personal.
Also see: the trust equation.
I learned about it from the excellent It Doesn’t Have to be Crazy at Work.