This area overlaps syntax and semantics. A feature is a piece of information associated with a word. Feature systems serve a number of goals. Features have a name and a value. In this case the name is AGR and the value might be s or p.
Some verbs have several allowable complements.
See Figures 4.2 and 4.4 in Allen for more examples of complement structures. A head feature is one for which the feature value on a parent category must be the same as the value on the head subconstituent. This grammar could be expanded to show all the feature values. For example, rules 11 and 7 would become 11. Grammar 4.8 in Allen has the details for all the other rules.