what is a traveling wave antenna?

They are normally long transmission line with a number of bends and discontinuities such that when microwave power flowes therough it, radiations take place at those discontinuities. In these antennas, the phase at those discontinuities are very important. To obtain the input impedance match, another end of the line is terninated with another load (typically ~Z0) and hence they are lossy and broadband.

They are also made from waveguide with a set of holes down one side. It is all described by the same math.

On the HF frequency range they are wires many wavelengths long that are set at angles to each other so that the lobes in only one direction add. The famous rhombic antenna is one of them.

normal patch antenna is a standwave antenna.traveling wave antenna have matching load.
you can find the details in the book "handbook of microstrip antenna"