A double standard is when a rule, law, principle, way of thinking, or so on is not applied the same way to different groups. A common double standard occurs with gender. Think about how women are often subjected to a double standard in the workplace. If a woman is demanding or tough, she might be called a derogatory name. Yet if a man is demanding or tough, he might be called a complimentary name, like a leader.
With "Men's Needs," the double standard seems to center on gender as well. Chacko has many affairs. His mom is aware of his liaisons. "He can’t help having a Man’s Needs," she says. To help him carry out his affairs quietly, his mom builds a separate entrance to his room. This way, "the objects of his 'Needs'" won’t have to go through the entire house.
Again, the double standard seems to be centered on gender and sex. Chacko can have all of the sex he wants since he’s a man. Meanwhile, the women are mostly frustrated and unfulfilled.
Take Ammu, for example. She’s not having myriad affairs like her brother. She does have one affair with the communist Velutha. Yet this lone affair—with a man she loves—leads to Velutha's death and an even worse life for Ammu.
Again, a man can have multiple, seemingly meaningless affairs and not be punished. Meanwhile, a woman has one very meaningful affair and she meets a tragic fate.
It might also be interesting to think of "Men's Needs" in a more general context. Think about how Chacko gets to go off to England and learn while Ammu has to stay home. That, too, is a double standard. It let’s men have education and freedom but it doesn’t let women have the same education and freedom. It implies that women don't "need" to do such things.