The obsession aspect means that an alcoholic will continue to drink, even knowing that it will probably lead to problems, and somehow thinks that it will be different the next time.
The physical aspect or "allergy" refers to the physical craving that develops once alcohol has been ingested.
Whether that qualifies as a disease is debataable.. All I know is that the physical part can be avoided simply by not taking that first drink. The obsession, however, is much trickier to overcome.