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Generally means that he form of the equation does not change if we transform .
This is generally what we want from the laws of physics.
E.g. a Galilean transformation generally changes the exact values of coordinates, but not the form of the laws of physics themselves.
Lorentz covariance is the main context under which the word "covariant" appears, because we really don't want the form of the equations to change under Lorentz transforms, and "covariance" is often used as a synonym of "Lorentz covariance".
TODO some sources distinguish "invariant" from "covariant": invariant vs covariant.