The Wronskian and the term "fundamental set of solutions"

A fundamental set of solutions to a differential equation is the basis of the solution space of the differential equation. Put in another way, every solution to a differential equation can be written as a linear combination of these fundamental solutions.

Secondly, the Wronskian being non-zero at a point $t$, tells us that the two solutions are linearly independent at that point. For two solutions to be the part of the basis for a solution space, we require them to be linearly independent.

Lastly, since the differential equation you are working with is of second order, the fundamental solution set consists of two linearly independent solutions. These two linearly independent solutions span the solution space (and hence form the basis for the solution space).