Need Help Understanding MST Cutset Formulation
The first constraint makes sure the induced subgraph remains connected : there must be an edge between every pair of subsets of $V$ ; or in terms of graph theory,  for every cut, at least one edge must cross the cut. For example, if $S=\{a\}$, the constraint is
$$
\sum_{(u,a)|u\neq a} x_{ua} \ge 1
$$
and this imposes that $a$ does not end up alone.

The second constraint makes sure you end up with $n-1$ edges, which is a characteristic of a tree.