p^μ is the μ-th component of the vector p, and in an equation p^μ = m u^μ, μ is to be taken as a free variable, i.e. the equation is true for every μ. In relativity, Greek indices are taken to range over time and the three spacial dimensions (whereas Latin indices only range over the spacial dimensions).
This notation can be naturally extended to tensor products of vectors in the tangential and co-tangential spaces to the base manifold that is spacetime (simply called "tensors" by physicists): https://en.wikipedia.org/wiki/Einstein_notation
This notation can be naturally extended to tensor products of vectors in the tangential and co-tangential spaces to the base manifold that is spacetime (simply called "tensors" by physicists): https://en.wikipedia.org/wiki/Einstein_notation