If I bet five dollars on a horse, the stake is low. (The stake is the amount of money I've gambled.)
If I bet five hundred thousand dollars, the stake is high. That means, if things go wrong, I will lose a lot.
So
If I am a politician, and I take a big risk, maybe I could lose my job, my reputation, money, my family . . . Even though it's not an actual stake, we say "the stakes are high" because if my risk-taking doesn't work out, I will lose a lot.