$\partial _{\mu} $ denotes the partial derivative and $\partial _{\mu} \partial ^{\mu}$ stands for a sum using the Einstein sum convention, i.e. $\partial _{\mu} \partial ^{\mu} = \partial _0 \partial^0 - \partial _1 \partial^1 -\partial _2 \partial^2 -\partial _3 \partial^3$,
$m$ denotes the mass of the particle,
$\Phi$ is either the wave function of the spin $0$ particle if we use the Klein-Gordon equation in a particle theory, or describes the spin $0$ field if we work in a field theory.
Why is it interesting?
The Klein-Gordon equation is the correct equation of motion that describes free spin $1$ particles.
Layman
Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.