Gross energy includes energy consumption within the energy sector along with distribution losses; final energy is the energy that reaches your doorstep as fuel or electricity. In other words, losses in production and transport are not included.
For instance, gross electricity consumption in Germany was nearly 600 terawatt-hours in 2011, whereas net power consumption was reported at around 535 terawatt-hours. The “missing” 60 terawatt-hours were consumed by power plants themselves or lost in power lines. See also: primary energy.