Assuming these animations are prepared before the taping then the audience can see them on monitors to the sides of the stage.
However, it seems more likely that these are added in post-production but I can't find a definitive answer, although this comment (from the article mentioned below) seems to indicate that these may be handy already.
...and finally time for the show to officially start. Colbert hopped on stage and began with his monologue. The whole taping ran smoothly, with Colbert only having a minor flub during the first few sentences and restarting from the top. Other than that, what we saw at the Ed Sullivan theater is almost exactly what we saw on TV. The entire taping ran about an hour to an hour and a half with pauses for commercial breaks during which the band played to keep the crowd energized.
There were some things that didn’t make it to the actual show. Some of the awkward pauses during the guest interviews were cut short or small bits that didn’t land with the audience were snipped out of the episode.
There's a whole article on what it's like to be in the audience which includes a more recent picture (2015) [Ignore the big red arrow] also shows the monitors.