In order to answer this question, we have to consider two situations:

a) The object could be at rest in our reference frame.

b) The "object" is never at rest in any (physically realizable) frame of reference.

An electron and a tennis ball belong to situation (a), where as a photon belongs to situation (b)

Let us assume that two masses exist, the mass when object has zero speed 'm0' and mass 'm' when object has speed 'V' as observed in our frame of reference.

When the object has zero speed, it is at rest (as observed by us or by someone accompanying the object), and so 'm0' is called the object's rest mass. It is an intrinsic property of the object.

For instance every electron has rest mass m0=9.11 x 10^-31 Kg.

If we set into motion a tennis ball that is initially at rest, the ball acquires kinetic energy, the energy associated with motion.Its energy increases.

From the equation E=mC2; it implies that increase in energy will correspond to increase in mass too. We deduce that ball's inertia increases. Thus the mass 'm' of moving ball is greater than the rest mass 'm0'. Hence m>m0 holds for any object with kinetic energy.

In 1905, Einstein summarized his theoretical discovery with sentence,

" The mass (i.e. the inertia) of a body is a measure of its energy content.