What is a guided mode?
A mode is a configuration of the electromagnetic field that is stable as the system evolves in time according to Maxwell's equations. Mathematically, it's an eigenstate of the differential equations and boundary conditions describing the system.
A guided mode is a mode that is confined within a guiding structure of some kind. For example a metallic waveguide, an optical fiber, or a photonic crystal.
It's contrasted, for example, with a free-space mode (by which electromagnetic waves propagate unguided in free space) or an evanescent mode (which don't actually propagate due to exciting the structure below the cut-on frequency, but which can couple power between other waveguides if the structure with the evanescent mode is short enough).