How does separation of powers and checks and balances support democracy?

Both of these limit the amount of power one individual or a small group of people can have. This supports democracy because it is against Dictatorship and oligarchy.

Separation of powers gives different powers to different branches of government. This means that no branch has the power to do everything. Checks and Balances are put into place so that the different branches of government hold each other accountable for what they do.