To simulate is similar to imitate. In the passage, the machine allows the turtles to move their legs as if they were swimming. It copies the conditions turtles need to swim.
Simulators can be mechanical, as in the example, but there are also virtual simulators which are used in all kind of experiments, training, and leisure. Think of videogames or flight simulators.
The checks and balancing system provides each branch of government with individual powers to check the other branches and prevent any one branch from becoming to powerful.
