The weak interaction is puzzle piece of considerable importance in our current understanding of particle physics. The standard model of particle physics explains the fundamental forces of nature in terms of interactions between a discrete set of elementary particles that fit into representations of various symmetry groups. For example, the strong nuclear force is described by an interaction mediated by massless particles called $gluons$, that fit into a symmetry group called the special unitary group in 3 dimensions, or SU(3) for short.
As it turns out, the electromagnetic force and the weak nuclear force are actually different manifestations of the same fundamental interaction, termed the electroweak force. As the story goes, there existed two symmetry groups in the early universe, one for the strong nuclear interactions, SU(3), and one for the electroweak interactions, U(2), (let's just put gravity aside for now).
Suddenly, a constant scalar field, namely the Higgs field, acquired a non-zero vacuum expectation value. Due to the way the Higgs field coupled with the U(2) symmetry group, the transition to a homogenous non-zero vacuum expectation value spontaneously broke the U(2) symmetry. The left over remains of the U(2) symmetry were arranged into a U(1) symmetry (that we now call electromagnetism), and three bosons that were endowed with mass by the Higgs field. These three bosons are now called $W^+$, $W^-$, and $Z$; they are the mediators of weak interactions.
Beyond their origin, weak interactions are quite interesting for the role they play in flavor changing. In the standard model, the weak interaction is the only interaction which allows elementary fermions, namely leptons and quarks, to change their flavor. When an element undergoes radioactive decay, it is due to one of the quarks within the nucleus changing its flavor through the weak interaction. By these means, the richness and complexity of the elements that make up our universe is dependent on the weak interaction. Additionally, the only way neutrinos can even interact with matter (besides gravitationally) is through the weak interaction.
I find it hard to fathom a universe that is anything like our own without the weak force.