Question: I am currently reading my text, for my electromagnetics course, and we are discussing guided waves. The text casually mentions the term "guided modes", and never really defines what that means.

Answer: 
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).
I would typically use "guided mode" to refer to a mode moving down a waveguide. For example, the LP01 mode of an optical fiber would be a guided mode. The opposite of a guided mode would be a mode in free space.

There may be other uses depending on context however.