Der Vater hat seiner Tochter eine Email geschickt.

The father (nom.) sent an email (acc.) to his daughter (dat.).

This sentence shows case being applied to nouns, der, seiner and eine being the indicators not only of the gender of their respective nouns, but also of their case, something which English can only indicate with word order. But look at this variant:

Seiner Tochter hat der Vater eine Email geschickt.

This sentence means the same as the former although the connotation is different, i.e. it was his daughter he sent an email to and not anyone else. The forms seiner and der clearly indicate who is doing the sending (the subject or nominative) and who the email is being sent to (the indirect object or dative). One advantage of case, as this simple example illustrates, is that it can give the speaker a greater choice of word order.

English has only preserved separate case forms in its pronouns, i.e. ‘I/me’, ‘he/him’, ‘she/her’, ‘we/us’, ‘they/them’; only in the second person, i.e. ‘you/ you’, is no distinction made any more, although previously it was ‘thou/ thee’ and ‘ye/you’. English uses ‘me’, ‘him’, ‘her’ etc. in both the accusative and the dative, e.g.

Ich habe ihn zu Hause besucht und ihm einen Scheck für €55 gegeben.
I visited him (acc.) at home and gave him (dat.) a cheque (acc.) for 55 euros.

The difference between ‘who’ and ‘whom’, which is now waning in English, is also an example of case, i.e. nominative versus accusative/dative, e.g. Who lives here?

Wer wohnt hier?
Who(m) did you visit in Berlin?
Wen hast du in Berlin besucht?
Who did you give the cheque to?/To whom did you give the cheque?
Wem hast du den Scheck gegeben?

The fact that ‘whom’ is fast dying out in English provides a living (just) example of the fate of case distinctions in English. But the point is that these distinctions are still very much alive and kicking in German and contribute to what English speakers i nd dificult about learning German. But once you have got your mind around the concept of case, it is extremely logical and getting it right is one of the great satisfactions of learning German. In German, case endings don’t just apply in the above instances. Adjectives take case endings, and verbs and prepositions can require that the pronouns and nouns that follow them take either the accusative, dative or genitive case, e.g.

Unser alter (nom. m.) Nachbar hat einen sehr netten (acc. m.) Sohn.
Our elderly neighbour has a very nice son.

Er hat mir geholfen. (The verb helfen takes a dative object.)
He helped me.

Meine Frau ist böse auf mich. (böse auf  acc.  angry with)
My wife is angry with me.