According to wiki, the convex hull can be mathematically designated by
$$\mathrm {Conv} (S)=\left\{\left.\sum _{i=1}^{|S|}\alpha _{i}x_{i}\ \right|(\forall i:\alpha _{i}\geq 0)\wedge \sum _{i=1}^{|S|}\alpha _{i}=1\right\}.$$
Can someone please tell me what $x_i$ is? According to wiki, it is supposed to be a point. Then shouldn't $x_i$ be a set of coordinates? Or is it a single value? If so, how is the single value obtained?
You have a set of points $x_1, x_2,$ etc. In the plane, as a 3-point example (i.e., $S$ is a three-element set) you might have $$ x_1 = \pmatrix{1\\3}\\ x_2 = \pmatrix{2\\5}\\ x_3 = \pmatrix{-1\\4} $$ The convex hull of those points (according to that formula) consists of all points that can be expressed in the form $$ 0.2 \pmatrix{1\\3} + 0.3 \pmatrix{2\\5} + 0.5 \pmatrix{-1\\4} $$ where the coefficients ($0.2, 0.3, 0.5$ in this example) must all be nonnegative (as these are) and must add up to one (as these do).