Space-time diagram showing the world lines of 8 galaxies that are currently 2, 4, 6, 8, 10, 14, 16, and 18 Gly distant. Notice their trajectories all start at the Big Bang and follow the classic a(t) shape, turning from deceleration to acceleration around 9 Gyr. In red are shown the light-paths from events occurring TODAY in each of these galaxies. Nearby, the light arrives with little delay caused by expansion, but in the more distant galaxies the light has to "struggle" to overcome the local expansion of space -- for example the galaxy at 14 Gly is currently receding at near-light speed, so its light doesn't make much headway initially, though ultimately we do see the event at about 52 Gyr. Notice that beyond about 15 Gly, the light never gets to us -- it is carried further away by the accelerating expansion. That boundary is called the event horizon, and currently it is about 15 Gly distant. The dashed line shows the event horizon distance at all times in the past and future. Notice that once dark energy dominates and we have exponential expansion, the event horizon stabilizes at about 15.5 Gly.
Figure from Whittle's (upcoming) undergraduate cosmology text.