Meaning of $\lambda$ on convex fnction definition

Question

What is the meaning (pratical/visual example) and significance of $\lambda$ on the definition of a convex function and why is it set on $[0,1]$?

Answer 1

It parameterizes the line segment between two points. For example, part of the definition is $\lambda x_1 + (1-\lambda)x_2$. For $\lambda=1$ this is $x_1$, while for $\lambda=0$ this is $x_2$. For $\lambda=0.5$ you get the midpoint.