The equation you've written isn't quite right. The Del symbol should be squared, and the $V$ (which doesn't represent the velocity) shouldn't be squared.

Once you've made these changes, the equation is a second order differential equation satisfied by the wavefunction of a particle, $\psi (x)$. Here $x$ represents the position of the particle, and can be a scalar (if the particle is moving along a line) or a vector (if the particle is moving in two or three dimensions). The wavefunction is a complex-valued function, and the integral of its modulus squared over a given region represents the probability of finding the particle in that region. Thus the integral over the whole space is 1.

In one dimension, the del squared symbol is the second derivative operator $d^2/{\mathrm{dx}}^2$, and this operator acts on $\psi (x)$. In three dimensions the del squared operator is $(d^2/{\mathrm{dx}}^2+d^2/{\mathrm{dy}}^2+d^2/{\mathrm{dz}}^2)$. Here, the $d$'s should be curly, as they are partial derivatives.

$V$ is another function of $x$, and represents the potential. If $V(x)=0$, the particle is said to be free; if $V(x)=m(\mathrm{wx}{)}^2/2$, the system is called a harmonic oscillator. There is another potential commonly encountered which is that of the hydrogen atom. I suggest you look this up if you're interested.

I hope this is of some help. Please write back if you have any further questions.