Constant moisture with adequate drainage is probably what they mean. As the plant gets established, it will require more water, but as it get larger, they're fairly "drought" tolerant. Depending on your soil, some suggest the addition of a soil amendment like compost, but it isn't essential. Dig a large hole to accomodate the roots spread and I suggest applying a good organic mulch such as chipped bark and woodchips after watering it in well. Most of the specimens I've seen and the one I have in my garden is in part shade.

Best of luck!

Riz

Well, part shade has many different faces.
For example, my 'Taiyo' was originally sited in full sun from 8am till 3pm. As hemlocks in background were growing it become more and more shaded and now get sun only from 9am till noon. As a result almost 6' tall absolutely healthy mature plant produced only 3 (three) flowers this year.
So far I still didn't figure out where to move it and decided to remove several hemlock's branches to open it a little bid, but I know this is just a temporary solution.

Part shade is a compromise position for a tree peony. They will thrive in full sun in northern states and do better than a more shaded spot. Unfortunately the flowers don't last long in full sun, so take your choice :)

The root system on these plants goes very deep, hence they are drought tolerant. The roots need constant moisture but that may mean constant moisture three feet deep in the ground! Provide plenty of water during the spring when they are leafing out and flowering, then an established plant should make it through the summer with just a nice mulch. They absolutely don't want to be left in saturated soil so provide good drainage. That might mean that you need to provide more water in the first couple of years while the root system gets itself established.