Differentiation between subjects and objects has a significant impact on the way we speak, so it is important to understand what they are.
The subject of a sentence is the person or thing referred to as carrying out or performing the action described by the verb. For example, in the sentence ‘The cat scratched the curtains’ – the subject of the sentence is the cat, because he was the one who did the scratching. The first thing to do then, is to identify the verb. Then ask yourself ‘who or what is performing the activity represented by this verb?’ The answer is the subject of the sentence, and this can be any type of noun (proper noun, noun, noun phrase, or pronoun).
Often, but not always, an action as described by a verb, is performed on, to, or for someone or something: the object. In the above example, it was the curtains that were scratched by the cat, so the curtains are the object of the sentence. To identify the object then, ask yourself who or what was affected by the verb's action – again, the object is always a type of noun.
By the way, if a verb requires an object before it will make sense (eg. the verb ‘to sell’ - something that is sold has to be sold to somebody), it is known as ‘transitive’. If it is not really possible to use an object noun with a particular verb (eg. ‘to arrive’), the verb is said to be ‘intransitive’.
One example of how subjects and objects affect word choice in English, is seen in the difference between the words ‘who’ and ‘whom.’ The word ‘who’ should only ever be used when referencing the subject, and ‘whom’ when referencing the object (‘who does what to whom’) – although this rule is gradually being eroded from the English language, so that the word ‘who’ is beginning to be accepted as a correct way of referring to an object (the technically incorrect use of ‘who’ as an object often sounds more natural, and conversational).