I know nothing of Russian (Я не знаю ничево в русскаям языкам… which proves my point); but the same polysemy occurs in Greek, and Philip Newton’s answer to Greek (language): Why do we say “παρακαλώ” when answering the phone or saying ‘you’re welcome’? makes sense to me: “please don’t mention it” (“please don’t abase yourself so much as to thank me”).
Intriguingly, the African American use of Nigga please! goes in the completely opposite direction: not an expression of humility, but of exasperation (“please don’t offend my honour/my common sense”)
Emil Manukyan is right about words meaning lots of things depending on their context, though it’s an exaggeration to say it could mean whatever you want: the meaning is still traceable back to “being well-disposed”.
But don’t quote Saussure, that’s just vague theoretical underpinnings. The way to make sense of this is conversational implicature. As in so much else about language, it was Grice that led the way on this.