Invariant in relation to any physical quantity means that this value is independent of reference frame in which one observes the given quantity.
E.g. invariant mass denoted in physics by m is for a given particle independent of its reference frame in which this particle is observed. This independence is achieved by dividing the relativistic mass (the measure of inertia of the particle) by γ factor.
So if velocity of a particle is v one gets invariant mass of the particle by dividing relativistic mass of the particle M by γ factor as in m = M / γ, where γ2 = 1 / (1 − v2 / c2), v is velocity of the observed particle, and c is speed of light in vacuum.