The term ephemeris (plural: ephemerides) refers to information listing the positions of some body in the sky over time, e.g., the Sun, Moon, or a planet. Traditionally, it might be a table relating equatorial coordinates to a world-wide standard time. In the computer age, applications combine the use of tables and calculation to adapt the listing to any time and/or Earth location, perhaps listing horizontal coordinates. (Regarding the use of singular versus plural, I believe the singular, ephemeris, has been used to refer to a reference book covering many visible bodies with the plural suggesting ephemerides refers to more than one such book. But the plural is sometimes used to mean the information on multiple bodies.)
The term fundamental ephemeris refers to information on a body's location in three dimensions, such as a planet's location over time, i.e., the kinematics of its orbit. The term solar system ephemerides (SSE) refers to the position of the bodies of the solar system. Such information is absolutely vital for spacecraft navigation, and also has an effect on observations of more distant events, the position of the Earth having the obvious influence (parallax), and other bodies having slight influences relevant to high-precision astrometry, in light of general relativity. Pulsar timing array efforts have a need for additional precision and are carrying out efforts to improve it.