As the examples in (1) above show, verbs like neglected must be followed immediately by a noun phrase called the direct object.
(4) Bob kicked John.
In (4), John is the direct object. In this case, which is the prototypical situation, the direct object is used to indicate the thing affected by the verb.
Verbs that have direct objects are known as transitive verbs. Note that the direct object is a grammatical function rather than a form. That function is usually filled by a noun phrase.
One useful test for transitive verbs is to see if you can change the sentences in which they appear into passive equivalents. The direct object of the active sentence becomes the subject of the passive version:
(5a) The fans applauded Jennifer's performance. [active]
(5b) Jennifer's performance was applauded by the fans. [passive]
If a sentence can be made passive, it is transitive. Be aware, however, that a small subgroup of transitive verbs (e.g., cost, resemble), do not have a passive equivalent. So if you cannot make a sentence passive, the verb may not be a transitive verb, but you need to check more closely.
We will label transitive verbs VT, which stands for "verb-transitive."
 When we talk of the usual range of meaning for the direct object, we are indicating its semantic function, or thematic role as it is often called. The usual name given to this particular role is the patient. We won't have much to say about these semantic roles, but they should not be confused with grammatical roles like direct object. Note also that the direct object actually plays a much wider range of roles than the patient, but in these cases, it still has the same grammatical properties as the central cases in which the NP is a patient.