A resonant antenna produces feedback that is in phase with the applied signal.
For a more intuitive example, consider a mechanically resonant structure, like a tuning fork. If the fork is struck, a mechanical wave travels through the fork's structure. Some of the energy in this wave is lost as sound to the air, but most of that kinetic energy eventually propagates back to the point where the fork was initially struck.
The time it takes for this to happen determines the resonant frequency of the tuning fork and the note you'll hear when its struck.
If you were to repeatedly strike the tuning fork at this frequency, you'd find it would be "softer" than it would be at other frequency because right at the instant you're striking it, the fork is vibrating away from the striker. That is, the feedback is in phase with the applied signal.
Resonant antennas are analogous for electromagnetic waves. Consider a resonant dipole: each leg is tuned to be electrically a quarter wavelength long. The time it takes for the wavefront to travel from the feedpoint to the end is a delay of 90 degrees, and back from the end to the feedback another 90 degrees for 180 degrees in total. The time it takes this to happen is the time it takes the phase of the driving signal to move 180 degrees.
Because the feedback from reflections within the antenna is in phase with the applied signal at the feedpoint, the antenna is resonant.