Given $n+1$ control points, B-spline blending functions are polynomials of degree $d-1$, $(1<d\leq n+1)$.
This much is easy to comprehend.
Now comes the part I am not able to make any sense of.
Each polynomial function is defined over $d$ subintervals of the total range of $u$. The selected set of subinterval endpoints $u_j$ is referred to as a knot vector.
What is the purpose of knot vector? What is its physical significance?