Moss plants form spores; minute, invisible, typically one-celled, reproductive units that are carried off by the wind and into your pots.
Mosses belong to the Bryophytes. Bryophytes are embryophytes; i.e., non-vascular land plants. They are spore-producing, rather than seed-producing and they do not bear flowers.
The leafy moss plant you are describing is the sexual phase of the moss life cycle. When mature, most mosses develop sex organs. Under wet conditions, sperm cells are released from male sex organs (antheridia) and swim to the female organs (archegonia), attracted by a chemical released by the female organ. After fertilization, the egg cells that are embedded in the female organ form a spore-producing plant. This consists of a stalk with a spore capsule and stays attached to the parent moss plant. As the spore capsule matures, it releases its spores into the air, and then dies. If moss spores fall in a damp place, they germinate and grow into leafy moss plants, and the cycle is completed (Fig. 1).
Hence, to answer your question - moss appears in your pots when spores land into it and enough water is available for their outgrowth.
Fig. 1. Reproductive cycle of moss. source: Encyclopedia of New Zealand