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 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 factor.
So if velocity of a particle is one gets invariant mass of the particle by dividing relativistic mass of the particle by factor as in , where , is velocity of the observed particle, and is speed of light in vacuum.