Extracellular Space is essentially referring to a part of a multicellular organism ( for us in neuroscience, this will only be for humans ) usually outside of the plasma membranes of the cell and occupied by fluid.
For our case, this is the space between the cells in the brain. This space is filled with Cerebrospinal Fluid (CSF), which is a clear, colorless body fluid found in the brain and spinal cord. It is produced in the choroid plexuses of the brain. The CSF acts as a cushion or buffer for the brain, providing basic mechanical and immunological protection to the brain inside the skull.
note: i am no biologist, so this is not my field of expertise by any means.