"Step up your game" means to improve the way you play as Ruthi stated. When the term "step up" is used in English it usually refers to improving in stages or "steps.". Thus, playing with better competitors or players is going to improve your game each time that you do it in order to... "step up your game."May 8, 2017

any better translation? I saw this one in Google

Translated just as understood. I don't know if there is an equivalent Russian idiom or a motto.

I have different understanding. smth like работайте над собой

Mikhail is right. GAME is figurative here. It means to work on yourself, improve your skills, make yourself more competitive and relevant at work, in the way you talk to women, etc. especially under the threat of new competition: A: Have you met the new guy in accounting? B: No, but he’s all they talked about at lunch today. Apparently management is very impressed with his experience and degrees. We’re going to have to step up our game!

Ok, good to know. Thanks, Uly!

😉