The accusative case has a number of uses. We will begin with two of these; its use as direct object, and the accusative following a preposition.
1) The accusative case is used for a noun or pronoun which is the direct object of a verb.
In the sentence we discussed previously
Ο απόστολος βλέπει τον προφήτην.
The apostle sees the prophet.
the direct object is the object (in this case, the person) which is seen: the prophet. So 'τον προφήτην' is in the accusative case.
Here's another example, taken from John 3:16:
τὸν υἱὸν τὸν μονογενῆ ἔδωκεν
the son the only-begotten he gave
(he gave the only-begotten son)
God gave ('έδωκεν') the son ('τον υιόν'): 'the son' is the direct object of the verb 'gave', and is put in the accusative.
ο υίός . . . . . the son (nominative)
τον υιόν . . . . the son (accusative)
This is not the only use for this case, however.
2) The accusative is used following certain prepositions, in a prepositional phrase.
These are prepositional phrases:
in the house
with the apostle
over the hill
The preposition can be thought of as expressing some kind of relationship. In the sentence
The prophet is with the apostle.
the preposition 'with' indicates a relationship between the prophet and the apostle.
'Mary is in the house' also expresses a relationship - in this case, between Mary and the house.
In Greek, the noun or pronoun which follows a preposition is put into one of the non-nominative cases; i.e., into the accusative, the genitive, or the dative.
The preposition 'εις' for example ('into') is always followed by a noun/pronoun in the accusative:
Η Μαρία έρχεται εις τον οίκον.
Mary goes into the house.
The preposition 'εις' is always followed by the accusative. Other prepositions, however, may be followed by more than one case, with a resultant difference in meaning. For example, when the preposition 'κατά' is followed by the accusative, it can mean 'according to':
κατά τας γραφάς
according to the writings (Scriptures)
But when 'κατά' is followed by a noun/pronoun in the genitive, it means something else, generally 'down from' or 'against'. For example (from 2 Corinthians 13:8):
κατά της αληθείας
against the truth
Clearly, it is important to recognize this difference in the use of 'κατά', since 'against the truth' would mean something entirely different from 'according to the truth'.
A bit more on the accusative next time. Χαίρετε!