1. to move quickly away from someone or something If a big truck bears down on you from behind, this powerful car can leave it in the dust. 2. to replace someone or something with something new This new computer virus left last year's killer virus in the dust.
By the way, when asking a question or posting a thread, you'd better offer supporting context. Hope it helps.
There is a Mandarin term which uses the same analogy: 望尘莫及 [望塵莫及]
The difference between this Mandarin term and the English term "leave something/somebody in the dust" is
1. the POV (point of view).
望尘莫及 is from the viewpoint of the one who can't keep up (the one who's left in the dust), and
"leave somebody in the dust" is from the viewpoint of the one who is 遥遥领先 [遙遙領先]
2. figurative versus literal.
望尘莫及 can only be used figuratively. eg 他的成就让我望塵莫及 (but not 我的跑车让那辆货车望尘莫及 [我的跑車讓那輛貨車望塵莫及]); while
"leave somebody in the dust" can be used both figuratively and literally.