Both words are used in the context of talking to someone for the first time. "It is good to meet you," politely acknowledges the interaction. "It is good to know you," does the same, but implies that the speaker has a greater interest in the recipient and perhaps wishes to learn more about the person.

To know something is to have memory of something. "I know where my bed is." "I know what time it is" but meet is an action where two things come together. "Let's meet in the park" "I want to meet a girl at the party"