What are the functions of political parties today?

It depends upon the country.

For example, in Burma, which is ruled by a military Dictatorship, political parties have NO power, but decrease some anxiety in the population, by pretending that there is democracy there. Similarly for countrie ruled by absolute monarchies.

is America a real democracy, when 26% of people can decide the government, as 50% of the people don't bother to vote?

Political parties should not be confused with power entities. Often the functions of political parties are merely symbolic in today's world.