代 has the overarching meaning of replacing, representing something with something else.
Decade
A special use of this counter is to denote a decade: like "the 90's" etc, or for the time of someone's life: 'my teens, my twenties.'
10代の頃によく怒られたよ。 People often got angry on me in my teens.
私は二十代の頃沢山旅行をしました。 In my twenties, I traveled a lot.
70年代の音楽が好きです。 I like music from the 70's.
Money earned
仕事とかの給料と料金とかは「~ {代|だい}」と言う表現です。
バイト代 The money you get from a side job: