What is force? It is the transfer of momentum with respect to time. Momentum is the product of mass of a body, and it relative velocity with respect to something. If we imagine, for once, our world made up of tiny uniform particles, then we can take the mass of one particle as one unit mass. This simplifies the situation, as the momentum, 'mass x velocity' becomes, velocity x 1 = velocity. So, when two such particles collide, they exert force on each other.
Or, literally, the faster particle loses a bit of its velocity and the slower particle gains the same with respect to time.
You are asking- " why does an object remains in a state of constant motion if no force acts on it".
This question is same as asking " Why does a unit mass particle has a constant velocity if it is not gaining some velocity."
For some reason, relative motion of a particle in space is a conserved constant. A particle does not gains velocity until some other particle loses the same amount of it. This is the same as the fact that a shopkeeper gains money if some customer loses the same amount of money in his shop.
(Yes, of course money gets lost sometime, or damaged, with a net lose to humanity, but in the universe at least, it is not easy to lose your momentum with nobody gaining the same amount, instantly!)