One of the most interesting aspects of the English language is the ability to change the order of words and still end up with the same meaning such as 'John bought a book' and 'A book was bought by John'. You may recognise these as the active and the passive forms of a sentence, the passive sentence being the one where the object is given more emphasis than the subject as opposed to the standard subject-verb-object. But if we can easily shift the object and subject around, how do we recognise which one is which in any given sentence?
The key actually lies with the verb. If we want to say that a hearty chuckle was let out by John at someone called Mary (in far less words of course!) we might say 'John laughed at Mary'. Here, laughed acts as a bridge between Mary and John indicating that what comes before the verb acts on what comes after the verb. This is called a transitive verb. If we were to swap the subject and verb however we come up with 'at Mary laughed John' we have a sentence which kind of makes sense, but doesn't seem to sit right on the tongue.
Another form of verb is the intransitive verb which does not need an object to function so we can say things like 'John laughed'. Intransitive verbs are used extensively in the passive tense so we can use an intransitive from of the verb laughed to move around the subject and object so we end up with 'Mary was laughed at by John'.
So there you have it, a very brief look at how subject and object can be defined and the links they have to the different types of verb.
Adapted from: R.M.W. Dixon (1989) Subject and Object in Universal Grammar Clarendon Paperbacks