To cry crocodile tears is to pretend to be sad about something. Your brother may appear upset about burning your family's dinner, but you know he really wanted to order pizza — those are just crocodile tears he's shedding.
Crocodile tears is an old phrase, dating as far back as 1400. People once thought that crocodiles shed tears to lure prey, or in response to their own violence. That display of false remorse or sorrow is exactly what crocodile tears are; if you don't believe politicians care about poverty, you'll see their emotional speeches on the plight of poor people as nothing but crocodile tears. Real crocodiles do shed tears, but only because their eyes dry out.