I am studying [Bloch's theorem](http://en.wikipedia.org/wiki/Bloch_wave), which can be stated as follows:

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> *The eigenfunctions of the wave equation for a period potential are the product of a plane wave $e^{ik \cdot r}$ times a modulation function $u\_{k}(r)$, which has the periodicity of the lattice. In total: $\psi\_k (r) = u\_k(r)e^{ik\cdot r} $.* [Reference: Kittel - Introduction to solid sate physics.]
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I have some problems understanding Bloch's theorem in full. Can I view the wavevector $k$ as the actual, physical momentum of the electron, which moves in a periodic potential, i.e., does it define the wavelength via $\lambda = 2\pi/k$?
And how does this relate to the fact that all wavevectors can be translated back to the first Brouillon zone?