Why does a same word may have different meanings?

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In linguistics, the phenomenon you're referring to is called polysemy. The question of why polysemy exists is quite a philosophical one.

A classical view is to think of a word as a linguistic sign, and its meaning is the thing that it signifies. The meaning between the sign and the signified is something that is established through convention at the level of a speech community. For example, I could call the pencil on my desk a "krarsk", but we wouldn't really call that a 'word' in the normal sense unless it spreads to multiple people and becomes used more widely by convention across some broader community.

The existence of polysemy takes on a special light when looked at from this viewpoint. Each member of the community can attach a slightly different interpretation of the sign-signified relation. For example, one speaker might think that "krarsk" refers to all pencils, whereas another might think it refers more specifically to purple pencils (e.g., because the word frequently co-occurs with the word "purple" in actual usage). Such mismatches between different individuals' linguistic systems are often so subtle that they go unnoticed in day-to-day life. This creates variation across the community in terms of the exact range of meaning associated with that word. Over time, as generation after generation of children learn the word in question, the meanings of the word can evolve and proliferate. As an end result, words naturally acquire additional meanings over time.