Compliance is a term used to describe the suspension of the cantilever in a cartridge, specifically, how easy (high) or hard (low) it is to deflect, relatively speaking. Basically the same concept as how softly or stiffly a car suspension is sprung. Just as in the car example, the appropriate deflection rating will depend on the mass of the suspended body - in this case, the combined mass of the cartridge and tonearm. The higher the mass, the lower the appropriate compliance rating to match it, or for a low-mass 'arm/cart combo, a high-compliance cart is used. The main idea is that the groove modulations cut into the record should be vibrating the cantilever/stylus, not 'wagging' the 'arm/cart, and that this needs to happen while still maintaining agile tracking and minimum surface wear. Roughly stated, the history of compliance in carts has moved from early days of massive 'arms/carts featuring low compliances, to a middle period of greatly lowered masses that required high-compliance carts, to the situation today where most 'arm and cart masses ratings - and consequently cartridge compliance ratings - are considered 'medium' (though this is not universally true, or even precisely defined).
