There is a few questions that need to be answered in detail but in an easy way...
What does it mean to describe the 'plane of polarisation' of electromagnetic waves?
Why will some antenna have rods which are horizontal and some which are vertical? What does this have to do with polarization of electromagnetic waves?
Consider a straight line-of-sight between a far away antenna and you as observer. It defines an axis. Now picture an imaginary plane surface at right angles to that axis. It is the plane of polarization. Antennas generate EM waves whose E and B fields are mutually perpendicular to each other and also to the line-of-sight axis (the propagation axis). Hence those fields lie always in the above defined plane. Normally it's the E field that specifies polarization direction.
Suppose the distant broadcast antenna is an electric dipole or monopole pointing upward wrt terra firma. Then the polarization is vertical because the E field you receive will oscillate in the vertical direction and also in that plane. Obviously then any receiving antenna should have that same alignment i.e. polarization. Seen in plan view the fields radiate outward from the antenna as circular wavefronts which at large distance tend more and more to look like a 'flat wall' or plane-wave to an observer. In the same kind of way that the earth's surface appears overall flat to us but is spherical seen from space.
Similarly, if the electric dipole antenna lies horizontally, E field polarization is horizontal, lies in that same plane, but the plan view radiation pattern will not be as neatly circularly symmetric as for the vertically mounted dipole.
Another type of antenna is the 'magnetic' loop, which when the loop axis is pointing vertically, there is generated a plan-view circularly uniform E field having horizontal polarization. That's one typical broadcast antenna arrangement used for domestic free-to-air TV reception - the Yagi receiving antennas one sees on many roofs have horizontal polarization to suit.
Reason for preferring one polarization over another can vary a lot.
