Case.

Case is a grammatical means of indicating what role a given noun phrase plays in larger phrase or sentence.

A noun phrase in the Nominative case is typically the subject of a verb.

A noun phrase in the Accusative case is typically the object of a verb (or of certain prepositions).

A noun phrase in the Dative case is typically the indirect object of a verb (or of certain prepositions).

A noun in the Genitive case is typically the possessor of some other noun phrase.

A number of theories of natural language grammars in linguistics (Lexical Functional Grammar, Head-Driven Phrase Structure Grammar, Cognitive Grammar, Relational Grammar, among others) assume that the categories of subject and object  are universal linguistic categories (i.e. they exist in all languages).

There are two basic ways that languages can encode the grammatical relations of subject and object.  One way is via word order (more properly constituent order), and the other way is via case.  Lot's of languages (like German, and, to a lesser extent, English), use a combination of these two.

English is a SVO Language (Subject-Verb-Object).  Thus it is pretty easy to figure out what the subject and object of the English sentence are:

• The subject is the first noun phrase to the left of the main verb.
• The object is the first noun phrase to the right of the main verb.

Now, when you get into complex NP's and such you have to be a tad more careful, but rough-and-ready, this will do.  In the following examples, the main verb is underlined.  The verbs is and did are auxiliary verbs, they are there for grammatical reasons, but the meaning of the sentence is carried by eat. Note that there is only one possible interpretation for these sentences, the dog always ends up in the cat's tummy.  Notice, though, that there is nothing about the noun phrases that tells you this, except the order in which they appear relative to the verb.

1. The big cat ate the yippy dog.
2. The big cat is eating the yippy dog.
3. Did the big cat eat the yippy dog?

SVO constituent order is pretty common in the languages of the world, but other orders are possible too, another very common type is SOV (Japanese is this way,  So is German, to a certain extent, at least in subordinate clauses).  As long as everybody using the language observes the same basic conventions, it doesn't really matter which order is the main one in a language.

But it could be otherwise.  There are also a number of languages out there that are a lot less strict than English about word order.  German is one of those languages.