First Example:
Tina: Did you hear? I just got the project.
Alec: Really? I thought my proposal was a lock.
Tina: They liked mine better. Looks like you need to step up your game if you're gonna compete with me.
Alec: Don't get too cocky. You won one proposal, your first.
Tina: The first of many.
Alec: We'll see.
Meaning: To "step up (one's) game" is a phrase that means to improve one's skills or talents. This idiom is sometimes used in a somewhat joking manner between people who are competing, as Tina uses it above. Alternatively, it can also be used to commend someone on their improvement, as in the next example:
Vito: I heard you got a promotion?
Kate: Yeah, they liked my last couple reports and told me to keep up the good work.
Vito: Congratulations! You've really stepped up your game. I remember when you first got here, you seemed so lost.
Kate: I was lost! I was terrified someone would figure out at any moment that I had no idea what I was doing, and I'd get fired.
Vito: Well, you know what you're doing now. You'll probably end up being my boss one day.
