'Deep orbit' is an informal term used in science fiction to refer to an orbit distant from the body orbited. Being in deep orbit is generally an indicator that the orbiting body (generally a space ship) intends to remain hidden.
The more technical term would be a high orbit; high orbits are most often used, at the current date, for geostationary orbits (or at least geosynchronous orbits), so we generally use the latter terms. However, these high orbits used by planet dwellers are not really all that high -- a geostationary orbit is exactly 42,164 kilometers from Earth's center. In comparison, the distance from the Earth to the Moon is 384,400 km. Authors might be forgiven for wanting a bit of hyperbole to emphasize how very high some orbits might be.