Variational Quantum Eigensolver is an algorithm that allow you to find the lowest eigenvalue of an Hermitian matrix, whatever it might be. This Hermitian matrix in the case of quantum chemistry is the Hamiltonian of a molecular system. In fact, it is the electronic Hamiltonian since quantum chemists usually make an approximation known as the Born-Oppenheimer approximation.
A fundamental goal and equation of quantum chemistry is the time-independent, non-relativistic Schrodinger equation:
$$ H|\psi\rangle = E|\psi\rangle $$
where $H$ is the molecular Hamiltonian as mentioned above. This is an eigenvalue problem. It has been a great challenge for many years, mainly because of the exponential growth of the problem dimension, exponential growth of the size of the wave function with the particle number. Therefore, for most of the time, quantum chemist have to perform some sort of approximation, like Mean-field theory. But this leads to inaccurate solution. Able to calculate ground state energy at various geometry configuration of the molecular system allow you to build a Potential Energy Surface if you will. This allows you to predict many interesting chemical properties. Also ground state are natural state of a system, so a system will naturally settle in its ground state if it is not being perturb.