A plain planet is the oppose term to a Mountain Planet. It is a planet where altitude does not vary much. It might be covered by plains, low mountains, hills or dunes, but the altitude must not vary too much.
In our Solar System, we don't have rocky plain bodies. However, Jupiter's moon Europa is an example. Europa has a sub-surface global ocean that is responsible for re-modeling its surface and keeping it flat. Based on this model, we can suppose that a young, volcanic rocky planet, with a small crust floating on a vast ocean of magma can be a plain planet.
Another, hypothetical example, is of a planet without significant volcanism and tectonic activity, but with liquids flowing on its surface. Without internal forces to raise mountains, erosion will slowly take place and will erode all mountains, into a large plain, leaving only hills and small mountains. Also, strong winds can erode mountains and large cliffs, but they will create a landscape dominated by dunes.
Based on these two models, plain planets should exist around very new and old stellar systems.
If a planet does not have an active environment (liquids flowing on its surface and a thick atmosphere), meteor bombardment will slowly transform it into a mountain planet like Mercury.
There might be more ways a plain planet can form, that we don't know today.
If it is an Inner Planet, then solar wind might have wiped out its water and atmosphere. A plain inner planet will be more easy to terraform, because the amount of water needed to create oceans is far smaller then what we would need for a mountain planet. By adding water (from comet bombardments), we can easy create a Shallow-oceaned planet, but where oceans can cover more then half of the surface.
Another scenario is if the planet has already enough water. If a plain planet has the amount of water Earth has, it will become an Oceanic Planet, with only a few or no islands for settlers.
The third and best scenario is of a planet with just the right amount of water.
Without mountains to block air currents, winds will be much stronger. Large, global air currents will mix the hot equatorial and cold polar air masses. If the planet is tidal locked, the same currents will occur, only that they will mix hot air from the illuminated hemisphere with the cold air from the dark hemisphere.
Climate should be more predictable then on an Earth - like planet.
In the last scenario, that of an Outer Planet, the climate should not be different from other outer planets. Winds should be almost absent, the air will have a lot of moisture and there will be no deserts.
Core Activity Edit
If the planet has its shape because of powerful internal volcanism and tectonic activity, then it will be a place with strong quakes. Volcanoes will be common and sometimes the surface can break, directly exposing the internal magma ocean. In such an environment, Earth-like life forms will be exposed to toxic gasses reaching atmosphere from the interior. For settlers, there will be another major problem, since large buildings will be affected by quakes and large infrastructure will not be possible.
If the planet is old and the flat Geography is a result of long-term erosion, then it is possible that the internal dynamo is not working. In such a case, settlers will be exposed to radiation.
Terraforming a plain planet will require the same techniques needed to terraform other planets. The main difference is that, since air circulation is done more easy, a single Terraforming Plant will be enough.
Oceans will be shallow and this means that water currents will be different. Water in the same area will separate harder into different layers, while water in different parts of the planet will mix harder.
Vegetation and fauna will spread faster across the planet, because there are less natural barriers (no mountains) to stop it.