The Unbearable Lightness of Being is a complex read because of its philosophical themes, many characters, nonlinear plot, and political setting. Due to Kundera (the author) himself experiencing some of the 1968 political turmoil, the political setting is actually a bit incidental and secondary to the main themes.
The political setting can be broken into two fundamentally opposing groups: those for communism and those against it. The philosophical themes can also be broken into fundamentally opposing things: heaviness and lightness.
The novel makes a great case for how difficult it is to determine whether something falls into the lightness category or the heaviness category. The novel cites Nietzsche's concept of Eternal Recurrence (the concept that all of history has occurred and will occur again infinitely) as something that can be interpreted as "light." However, the novel acknowledges this to be a matter of perspective.
Though communism is highly oppressive (heavy) in practice, it can free all individuals of the burden of choice that comes with more freedom (light).
Democratic societies emphasize the individual and give them freedom of thought and choice (light), but that freedom comes with the potential burden of choice (heavy).