What does scalar phi represent in spacetime? Trying to understand one-forms and vectors via Schutz's A First Course In General Relativity.

His example uses a spacetime diagram, a scalar field phi, a curve (worldline) parametrized using proper time and the tangent vector (4-velocity). I think I understand, but I can't see the physical significance of the scalar field phi. In plain English, in the spacetime diagram, what does or might phi represent?
 A: Scalar field is a field of scalars (don't blame me, you invited Captain Obvious yourself). In other words, it's just a function on the manifold. If the manifold were the surface of the Earth (I hope you don't mind I move to 2+0 dimensions for a bit), it could e.g. be the ground temperature in certain moment.
Moving up to 2+1 dimensions, it can again be a field of temperatures but now with time record included. So, your curve $\gamma$ records your wandering around the globe and ${\rm d} \phi \over {\rm d} \tau$ just tells you how the temperature you experience varies both in space and time.
Moving up one further dimension still, a 3+1-dimensional field could be e.g. temperature anywhere in the atmosphere (and again also in time).
Now, in particle physics, scalar fields play a whole different role. They are not connected to familiar things like the temperature above and one instead has to think about them purely abstractly, relating them to things such as EM waves and photons. EM wave, after all, is just a vector field (meaning having spin 1).  Similarly, an electron is a particle associated do a Dirac field (which is a fermionic field with spin 1/2). Finally a scalar field has spin 0. I hear, one of the recently-gone-famous fields in this class goes by the name of Higgs :)
