A regime is the ruling government of a country. The amount of freedom and restriction that citizens of a country have can change from regime to regime.
Regime takes its militaristic and government feel from the Latin word regimen "to rule." A political regime has a negative association to it that makes you think of totalitarian governments. How did it come to mean "diet" or "program of exercise" as well? If you are put on a regime of exercise and healthy eating, you are ordered by a doctor to do these things and it probably feels like you're being ruled sometimes!