The term "democracy" can mean everything and its opposite. Without going all the way back to the Greeks, even the Communist regimes defined themselves as (popular) democracies.
We define democracy as a political system based on freedom of expression and free elections.
Democracy can be defined as the best (or rather, the "least bad") of political systems, but in most of the world, this belief does not exist, and therefore democracy is not possible, nor can it be imposed. Afghanistan, Iraq, and Palestine are examples of this.
I cannot say, however, whether democracy is the cause or the effect of our well-being. Are Western nations more prosperous because they are democratic, or are they democratic because they are more prosperous?