Hospitality is primarily about arranging for food and drink to be available to convention members. Sometimes it is provided as part of the convention membership, such as at a (Consuite/Hospitality Suite), or in a lounge for featured guests and panelists (Green Room). Sometimes it involves setting up arrangements for formal dining (Receptions), or for members to do their own entertaining in Room Parties.
More generally, it is a function that ensures refreshments are available to the members in appropriate quantities as needed, in a fashion that is in tune with the goals and the theme of the convention.
People working on hospitality often need to coordinate with the hotel for catering or for agreements regarding bringing in outside food. This process should be informed by an understanding of corkage fees and waivers.
Another feature that is having increased popularity is an Internet Lounge. Strictly speaking this would not be a place for food or drink, but it is a comfort place, of a sort.