'A field is not a real thing'. I think many physicists would dispute this statement. One can describe and explain a field in terms of the force interactions it has - between electric charges for an electric field for example. These forces have a strength and direction associated with position in the field and magnitude of the two charges which are an
interaction. (For electric fields and charges the force interaction, a non-touching force from a distance, is mediated by photons - a type of boson particle). An electric field is a vector field requiring three number to define it - position, force strength and direction.
So, one would say an electric field exists outside a charged hollow metal sphere but does not exist inside the sphere. The
thing is the region of space where force interactions between charges or between the field and charges happen. For the example of a charged sphere, there is the unbounded region outside the sphere and bounded region inside the sphere. In the former the field is of infinite extent albeit it decays with increasing distance.
I think what Lucien may have meant is that a field is not
really made up of field lines as is commonly drawn to represent a vector field. A field is continuous.
When Lucien writes
'The field is nothing in and of itself' I think he is saying that a field is not self-generating ie a charge must be present for an electric field and mass for a gravitational field. This follows from a field being a region where interaction takes place between charges or masses. Without them no field exists.
Here is a nice short piece by Scientific Amercian on fields: