3 Answers

Knowing something means that you can repeat or write the idea, technique, etc.  Understanding it means that you can answer questions about it, you can perform the skill (unassisted) and that you can explain it so well that another can learn it.  You have mastery well beyond one who simply knows it!  There is a big difference between the two...

Actually, knowing and understanding might have similar meaning, depends on the context of the word in a sentence.
Knowing something means to perceive it, to comprehend it exists. Understand might mean the same, but also it might mean the process that ends with knowing.

Here is an example in a sentence. People don't know or understand obama, if they did they would not vote for him.