Two closely related and in some ways opposite aspects of a sentence are topic and focus. They each need a more detailed write-up of their own; this one is only an overview of their relationship. Roughly, the topic is the already known information that the sentence is about, and the focus is the new information that is being said about it. But there are numerous overlapping distinctions here, and people use the words in various ways. It is not my place to provide exact definitions, but only to sketch the kind of distinctions being made. And it's going to sound awfully vague, sorry: the whole area is a mess.

There are several ways they can be marked: by intonation, by overt material such as the words 'as for' or 'it is' or Japanese wa, or by syntactic means such as fronting; or a combination of these.

Taken in isolation, a sentence like 'John was eating peanuts' said in a neutral way would probably have fairly equal stress on subject and object: 'JOHN was eating PEAnuts'. This is also how you'd read the sentence if it was the opening of a story. It introduces John, it's about him, and it's telling you what he's doing. But if part of the material was already known (the topic), the unknown material would get focused intonation by being given the main stress. This happens in answers to questions, for example:

Who was eating peanuts?
JOHN was eating peanuts.
What was John eating?
John was eating PEAnuts.
I'm using capital letters here to indicate a normal intonation, not an emphatic one. There is no reason to suppose there is any particular emphasis on the stressed element. Contrast with:
Mary was eating peanuts.
No, JOHN was eating peanuts.
John was eating walnuts.
No, John was eating PEAnuts.
Here we have the same distribution of focus and topic, but contrastive emphasis in addition. Whether emphatic or not, one element is new and has focus, and the rest of the sentence is given, and is the topic. We can't always neatly divide them between new and given like this: the introductory or isolated sentence 'John was eating peanuts' has no particular focus, and if we don't know who John is, it's all new.

One grammatical marker of a similar distinction is the choice of definite 'the' or indefinite 'a'. As an introductory element, something is definite if it's already known.

A farmer was leading a donkey. The donkey stopped and the farmer urged it on.
Here we could say the first sentence introduces a new topic with 'a', and the second carries it on with 'the'. But which is the topic, farmer or donkey? It could be either. In speech there might be a difference in intonation that told you which was going to be the topic; in writing you need to see how the story unfolds:
A farmer was leading a donkey. It stopped and the farmer urged it on.
A farmer was leading a donkey. He urged the donkey on when it stopped.
Definiteness doesn't have to be derived from a previous mention. Any of the following could be the opening sentence of a story, and they give different discourse effects as to what you are supposed to take as given, or background, and what you should focus on as foreground:
A man was climbing the garden wall.
The man was labouring to climb the garden wall.
The man climbing the garden wall paused half way up.
Another grammatical device to indicate topic and focus is placement of the prominent element in other than its usual place: either at the front or at the end. Fronting is common. In English essentially the same construction can be used for both focus and topicalization, and the difference is in stress both on the fronted prominence and in subsequent material.
The professor, she hasn't read this BOOK yet.
This book, I haven't READ it yet.
This book I haven't READ yet, but I'm going to soon.
The topic might or might not be bracketed off with comma intonation; if it is, it is likely there is a resumptive pronoun ('she' and 'it' in the examples) in the usual place for the constituent. This phrasing looks a bit odd in isolated example sentences, at least in English: but in real speech and text it does happen.

In many languages, such as Japanese, the topic is a normal grammatical constituent, and many or most sentences have an explicitly marked topic: see wa (by sekicho) for details.

When the stress is contrastive on the prominent element, it gives focus to it. In example sentences it's clearer if I add a contrasting clause after it:

THIS book I haven't read.
THIS book I haven't read, as I was busy with the OTHER one.
There is a roughly iconic principle that familiar material tends to appear early in the sentence, and new material after it. With no indication to the contrary, we would probably understand it that way. But focus fronting overrides this. Another way of bringing material forward is by changing the grammatical relationship between the actants: object becomes subject when you use the passive voice. But focus and topic are intricately entangled: the passive can be used for either effect.
No-one has read this book.
THIS book hasn't been read by anyone.
This book hasn't been read by ANyone.
Another strategy is to form a cleft sentence or pseudo-cleft sentence:
It is this book that I haven't read.
What I haven't read is this book.
These syntactic rearrangements or special forms normally carry a corresponding intonation; but note that intonation can always be used to mark focus elsewhere:
It is this book that Í haven't read.
What I haven't read is this book.
This book hasn't been read by anyone.
Extraposition, that is moving out of its normal place, is more usually to the front; but it can be to the end. The topic can be added to the end with comma intonation; and in a strategy called heavy shift you can place a large amount of material in final focus position even though a smaller amount of the same type would be ungrammatical there:
She hasn't read this book yet, the professor.
* She hasn't read yet the book.
She hasn't read yet the book with all the strange diagrams in it.

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