To show that you know something is to acknowledge it. Waving "hello" to acknowledge a friend and nodding your head "yes" to acknowledge that you agree with what's being said are both acts showing knowledge or acceptance of someone or something.
Dictionaries acknowledge that the word acknowledge has roots in the 15th and 16th centuries and is a combination of roots meaning "accord," "recognize," and "understand." Whereas "knowledge" is what you know, acknowledging is showing that you know. You might acknowledge that the world is round and that the moon is not made of cheese. You also can acknowledge, or give recognition, to the people who discovered these truths.