's is a common English contraction for many things. It is appended as a postfix to the end of words is the same manner as -ed, -ing, and -s, although in the case of 's an apostrophe is mandatory. In most cases this came about because people were lazy in their speech, and shortened their pronunciation of various short, unstressed words. These modifications to everyday speech have become entrenched in common usage, although according to the Oxford English Dictionary every last one of these usages are colloquial, poetical, or dialectical. Be that as it may, they are extremely common, and you cannot fully understand spoken or written English without mastering their use.
The most common contraction is of the verb 'is'. Hence, 'there is' becomes 'there's'. 'She is' becomes 'she's'. Just as the verb 'to be' is conjugated to form is, are, will, and am, the contraction can be conjugated; she's, they're, he'll, and I'm.
While it is generally obsolete, it is still common to use 's as a contraction of us in one specific context: the word let's ('let us'). This is an odd anachronism within the English language. It is apparently a holdover from a more polite era, and no longer follows common English form. The literal translation is "permit us", which can be confusing to ESL learners, who are likely to expect a simpler construction. While most languages have a simple, easily intelligible phrase along the lines of "we go", English requires one to say "let's go".
4. Occasionally it will be used as a contraction for 'has', as in "he's got a computer". Just as the verb 'to have' is conjugated as have, has, and had, the contraction is conjugated they've, he's, and (occasionally) I'd. (Note that I’d is more often a contraction of ‘I would’).
5. Informally, it is often used as a contraction for 'does'. This rarely makes it into print, but is common enough in spoken speech. 'What does' becomes 'what's' (e.g. "what's he know about it?" or "What's she do?") and 'when does' becomes 'when's' (e.g. "When's Parliament reassemble?")
6. You will occasionally see it used to mean 'it is'; "By my troth's not so good, and I warrant your cosin will say so." (Shakespeare Much Ado About Nothing III. iv. 9). This is not entirely obsolete, but it is uncommon.
7. In Scotland and the Northern UK you may hear it used as a contraction of 'as'. Examples of this are "as well's I can", "as soon's I can", "it gets so's you can't tell". EnochRoot quite correctly points out that this form is also used in the southern Appalachia of the US.
8. In the past it was use to mean 'God's' in oaths; in this case it is not used as a postfix, but as a prefix; "God's wounds" became 'Swounds, God's foot became 'Sfoot, etc. While this was once a very common method of swearing, the few oaths of this sort that are still in common usage today are generally no longer written in this form, e.g. zounds (God's wounds) and gadzooks (God's hooks)
Using 's to show possession:
We generally use 's to show possession. For example, if something belongs to Bob, it is 'Bob's something'. The pajamas that belong to the cat are 'the cat's pajamas'. The node that belongs to wertperch is 'wertperch's node'. This is a shortening of the Old English postfix -es , also used to show possession.
There are many fun rules surrounding this usage:
- Pronouns don't use this contraction, so you say "his node"; "their node" and "its node". It's, with an apostrophe, is only used for the contraction of 'it is', causing much confusion even among native English speakers.
- When speaking of something belonging to multiple entities, you move the apostrophe over one space: "the cat's pajamas" (pajamas belonging to only one cat) but "the cats' pajamas" (pajamas belonging to multiple cats).
I have not been able to find the reason for this convention. I speculate that at one point people may have been faced with the obstacle of saying "the cats's pajamas", and quite reasonably decided not to bother pronouncing the second s. Regardless, cats, cat's, and cats' remain homonyms, and the distinction is only apparent in written language.
- Traditionally, the possessives of proper nouns ending in s are also written with the apostrophe following the s; “Jesus’ disciples”, “Socrates’ writings”. This is changing, and it is now common to write it it the same way you would pronounce it; “Jesus’s disciples”.
- And finally, compound nouns are only given one 's. Thus we say "that is Dick and Jane's ball" not "that is Dick's and Jane's ball".
But what about making plurals?
Generally you do not add 's to make a plural. If you have more than one cat, you have 'cats', not 'cat's'. There are exceptions to this rule, but they are few and far between, and are not universally accepted.
Possible Exception #1: Numerals. It is okay to use an 's when talking about multiple numbers if you are writing the number instead of spelling it out. "Look at all the 1's and 0's!"
Possible Exception #2: Letters. Likewise, if you are using a single letter, its plural may be written with an 's. "Mind your p's and q's."
Possible Exception #3: Words used to refer to words. When using a word to refer to tokens of that word, you may use 's for the plural. "Aye's resounded throughout the room"; "Boo's filled the air".
Please note that while these pluralizations are considered acceptable by many, others disagree. If you are writing formally you should check with your professor, boss, or preferred style guide to see the preference within your field.
If you live in Holland, you may have noticed 's appearing in the middle of people's names; this is one of the many Dutch tussenvoegsels (surname prefixes); just as you might see Dick van Dyke or Jan de Vries, you might also see Jan 's Vries. Both de and 's translate loosely as 'the'. ('Van' might be better translated as 'of').