A basis for a subspace is a set of vectors that spans the subspace where no one vector in the set is "redundant" in defining the span. (i.e. the set is linearly independent)
What is a subspace: https://www.youtube.com/watch?v=JoeVHP_jg44&t=2s
How to tell if vectors are linearly (in)dependent: https://www.youtube.com/watch?v=L1ErFhSxIew&t=152s