Wave Propagation in Transmission Lines
The magnetic field around the wire corresponds to the current in the wire. More correctly, the magnetic field in the space between the wires corresponds to the current loop formed by the source, one wire, the sink, and the other wire.

The electric field between the wires corresponds to the voltage between the wires. If there's 10v measured between the wires, and a distance of 1m between them, then the field will be about 10v/m (varies with the position), with a conventional direction of from the positive conductor to the negative conductor. The direction isn't shown on your diagram, perhaps to avoid clutter, perhaps because the author thought it was obvious.

It's common to hear transmission lines described as wave guiding structures.