Can someone tell me what that little 3 means?

The 3 is part of the radical. It is asking what number is being multiplied by itself three times to get 64. 
For example:



What number is being multiplied by itself three times to get 27 (?)(?)(?)
(2)(2)(2)=8
(3)(3)(3)=27
The answer will be 27 for the example

For your question, 4 is being multiplied (4)(4)(4)=64