The indirect object of a verb phrase or sentence is a noun indicating the person or thing for which, unto which, or for whose sake the verb's action is performed. The indirect object may be inflected into a dative case, if your language supports such a thing. In English it is commonly indicated by the prepositions to or for.

Hence, in the sentence "John gave a dog to Mary", Mary is the indirect object, as the dog (which is the direct object, q.v.) is being given unto her.

In English, however, the indirect object may also be indicated positionally. The above sentence may be stated without a preposition as "John gave Mary the dog." To a native English-speaker this is not ambiguous, though I imagine it may be somewhat confusing to an English newbie.

A sentence with an indirect object may not always need a direct object. Thus, "John wrote to Mary" has Mary as indirect object, but no specified direct object. From our social background, we can infer that John wrote a letter, a postcard, an email, or something of the sort, to Mary.