"people rule" i.e. rule by the people
The etymological definition. This incudes both representative and majoritarian democracy.
The majoritarian definition, and probably the most common understanding of what democracy means.
a system by which rulers are elected
The representative definition, but includes straight majoritarianism. Virtually identical conceptually to definition #1.
a political unit that has (or purports to have) a democratic government
The nominal definition mainly used by States,
e.g. "Democratic Republic of the Congo."
the idea that all people are equal and that this should be reflected in social organisation; the absence of hereditary or arbitrary class distinctions or privileges
The egalitarian definition, rather unusual in modern speech.