In a penumbral eclipse, the Full Moon enters the Earth’s penumbral shadow. The light from the Earth is partially blocked, and the Moon grows dimmer.
In principle, a penumbral eclipse can be a partial penumbral eclipse (with only part of the Moon in the penumbra) or a total penumbral eclipse, where the entire Moon is in the penumbra; however, most penumbral eclipses are partial, since the penumbral shadow of the Earth is only about as wide as the Moon, so it’s rare for the Moon to fit entirely within the penumbra without entering the umbra (and hence making a partial umbral eclipse). Once in a while, though, it happens — about 1.2% of all lunar eclipses are total penumbral eclipses.
Most penumbral eclipses are pretty uninteresting, since the Moon is still quite brightly lit, except in the most advanced stages. Still, in a deep penumbral eclipse, sharp-eyed observers should see a subtle but distinct shading across the Moon at maximum eclipse. This will be quite obvious in a total penumbral eclipse.