Kropotkin was an anthropologist by profession, and this is shown by frequent references to this science in his work. "Mutual Aid" is in large part an attempt to rebut Darwinist arguments for the necessity of individualist egoistic action by demonstrating that mutually supportive, cooperative and altruistic actions are common among animals and in human societies. Kropotkin seemed to think that cooperation is part of human nature, so pervasive it is across different cultures and so resilient it is to attacks by the state.
He viewed the state as a force of atomisation because of its tendency to persecute specific associations. He saw it operating in an imperialistic way, colonising everyday life from above and outside and counterposing itself to the force of society and sociability as an everyday factor. The state is based on violence and control, and hierarchic forms and unnatural and oppressive. The state should therefore be overthrown or overcome, and replaced with social relations based on mutual voluntary cooperation in a series of federated associations.
His thought is best located within anarcho-communism. Although dated in some respects, it still holds up as a critique of sociobiology and of theories of the necessity of state power.
I don't know how it could come to mean "a stupid person" - I assume this is a Slavophobe appropriation of this rather amusing-sounding Russian name.
Anti-capitalist groups often unknowingly adopt a model of organisation similar to Kropotkin's, favouring small-scale voluntary groups which come together into larger federations for purposes of mutual support.