Separating power was not enough. The framers also armed each branch with weapons to fight the other two, on the theory that ambition must be made to counteract ambition.
Checks and balances are the specific powers each branch holds to limit the others. Beyond just keeping the branches separate, the Constitution makes them overlap, so each can block overreach by the rest.
The list is long. The president can veto laws; Congress can override the veto and can impeach the president; the Senate confirms or rejects appointments and treaties; the courts can strike down laws and executive acts; Congress controls the money. Each branch has a hand around the others' throats.
James Madison explained the psychology in Federalist No. 51. Since you cannot count on leaders to be angels, you design the system so that each official's ambition is set against the others. Ambition must be made to counteract ambition, he wrote. Self-interest becomes the guardrail.
It is deliberately frustrating. The friction means cooperation is usually required to get anything big done, and any branch reaching too far can be slapped back by another. The system runs on conflict, by design.