Telepathy, as it's name implies, is used for reading minds. The distance appears to vary between users, as Ninten and Ana are only able to read the minds of only a select few in front of them, while Paula can read minds miles away. Paula, unlike Ninten and Ana, can also contact the minds of people extremely far away. As such, she is able to telepathically communicate with anyone.
In Mother, both Ninten and Ana are able to use Telepathy, although this is only available in the field. It allows Ninten or Ana to read the minds of certain characters, such as Swimming Cats. It isn't a PSI that is used often, however.
 Mother 2
Paula Polestar owns Telepathy in Mother 2. As with Mother 1, it is seldom used. It is classified as an "other' type PSI. Telepathy helps Paula numerous times. The first is when Paula is kidnapped by Mr. Carpainter. She uses it to contact Ness, and later Jeff..