It's almost easier to consider what happens with two objects, then extend that to all of the objects in the universe.
In an elliptical orbit, the orbiting object gets closer to the orbited object at perigee, then further away at apogee. You could think of it as the two-body system is contracting, then expanding, then contracting, then expanding, etc, forever. If the mass of the universe is great enough that gravity overcomes the initial velocity from the Big Bang, then this is what will happen to the universe. Expanding or contracting just tells you where you are in the cycle, but the overall cycle of expansion/contraction goes on forever.
If an object is going fast enough (escape velocity), gravity can never slow the object's radial velocity to zero and the object just gets further away, never closer. It's radial velocity decreases, but the rate of decrease is always decreasing as well (it's radial acceleration). The two-body system is always expanding, but the rate of expansion is always slowing down. If the initial velocity of the Big Bang was great enough to overcome the gravitational force of the mass of the universe, the universe expands forever even though the expansion rate decreases.
If the expansion rate increases (as seems to be the case from observations), then some other force besides gravity must be acting on the universe. A repulsive gravitational force, dark energy, etc. are all things haven't been observed directly, but have to exist in some form to explain observations - in other words, they're theories to explain why we see an increasing expansion rate - something that can't happen due to gravity alone. Either something exists to cause an increasing expansion rate or else our observations are wrong for some reason (if the observations are wrong, then the reason for them being wrong would also have to be explained, so there's no free pass by just saying the observations are wrong).