I'm afraid there are no particularly easy answers to the question, but i'll give it a go.
First off, the wave function does not describe the "up and down motion". The conundrum all centers around the particle/wave duality problem. When physicists were trying to characterize light, some said it travelled in particles, because it was emitted and absorbed in discrete packets of energy. Others said it traveled in waves, because it showed diffraction grating patterns of cancelation. But the waves aren't really waves in the sense of going up and down--they merely behave like waves in some experiments. Later, de Broglie decided that since Einstein showed that photons had energy and wavelengths, he could extend the theory and say that electrons and other massive particles had wavelengths, too. But the entire idea is based on quantum mechanics, and doesn't really correlate to anything that you can think of in common sense terms.
As for the bonding/antibonding deal, again, it's all quantum mechanics. Schrodinger and Heisenberg each published descriptions on the probability of finding an electron at a certain place around the nucleus of an atom. If you take a look at someting called the Schrodinger equation, you can see an ugly polydimensional differential equation with crap like Plank's constant and the permittivity of a vacuum. All the n=1,2,3,4... numbers correspond to Eigenvalues to the eigenfuntion--that is, statistical distributions that satisfy the Schrodinger equation. When orbitals overlap, the resulting molecular orbital is any "linear conbination" of the atomic orbitals, meaning that you can either add the distribution functions to eachother, or subtract them from one another. When the functions are added, you get a lower energy (meaning more stable) bonding orbital, wherein ther is increased electron density between the nuclei, and the bond is stronger. When you subtract the functions, you can end up with places where the net probability of finding an electron is zero--a node--and this correlated to a high energy (unstable) anti-bonding orbital. Both orbitals are there, but they are only occupied if one or more of the electrons in the molecular orbital has an energy level that would place it in that particualr orbital. Long story short (too late!), the matter can only really be understood in mathematical terms, because it doesn't really mean anything that makes sense in terms of what we can perceive. Sorry. I'm also pretty sure that there are a number of people who have taken more physical chemistry than I have who see large errors in this explanation, but I'm doing my best.
As far as the point someone made about higher and lower energy level, you have to remeber that it's all relative. n=1 requires more energy to remove the electron from the atom (higher ionization energy), but generally it is refered to as a lower energy state, as it is a ground state to which an electron might go after releasing a photon from a higher (n>1) state.
