A Bitcoin address, or simply address, is an identifier of 27-34 alphanumeric characters, beginning with the number 1 or 3, that represents a possible destination for a Bitcoin payment. Effectively it is a 20-bytes long hash from the RIPEMD160 function of a public key encoded into alphanumeric characters. Addresses can be generated at no cost by any user of Bitcoin. For example, using Bitcoin-Qt, one can click "New Address" and be assigned an address. It is also possible to get a Bitcoin address using an account at an exchange or online wallet service.
An example of a Bitcoin address is 31uEbMgunupShBVTewXjtqbBv5MndwfXhb.
A Bitcoin address is like an e-mail address
Like e-mail, you can send bitcoins to a person by sending bitcoins to one of their addresses. A person can have many different Bitcoin addresses and, for increased privacy and as the only way to know what the bitcoins are received for/from, it is recommended that you use a unique address for each transaction. Most Bitcoin software and websites will help with this by generating a brand new address each time you perform a transaction. Some services provide a facility to request a new Bitcoin address for use with their service when desired.
When using a web site that accepts bitcoins or holds Bitcoin balances on your behalf, that website will assign a Bitcoin address to your account, so you can transfer funds into your account at the site. Very much unlike e-mail, this address may change every time funds come in so care should be taken when sending additional funds to a previously-used address. When you send Bitcoins to your account at a web site, they will usually be credited to your account at that web site after the transaction is confirmed.
Addresses can be created offline
Creating addresses can be done without an Internet connection and does not require any contact or registration with the Bitcoin network. The network starts tracking an address when it is first seen in a valid payment transaction.
It is possible to create large batches of addresses offline using freely available software tools. Generating batches of addresses is useful in several scenarios, such as e-commerce websites where a unique pre-generated address is dispensed to each customer who chooses a "pay with Bitcoin" option.
An average desktop computer can generate thousands of new Bitcoin addresses a minute. Addresses are created simply by generating random numbers and then performing mathematical operations to derive matching pairs of "public" and "private" keys. Because addresses can be created easily and at minimal cost, it is not uncommon to create temporary addresses that can be discarded if unused.
Addresses are case sensitive and exact
Bitcoin addresses are case-sensitive. Bitcoin addresses should be copied and pasted using the computer's clipboard wherever possible. If you hand-key a Bitcoin address, and each character is not transcribed exactly - including capitalization - the incorrect address will most likely be rejected by the Bitcoin software. You will have to check your entry and try again.
The probability that a mistyped address is accepted as being valid is 1 in 232, that is, approximately 1 in 4.29 billion.
If you would like to validate a Bitcoin address in an application, it is advisable to use a method from this thread rather than to just check for string length, allowed characters, or that the address starts with a 1 or 3.
Addresses have a "private key"
For most properly-generated Bitcoin addresses, there is at least one secret number known as a private key which is required for access to the funds assigned to that address.
When using a Bitcoin client, private keys are typically stored in the wallet file. The private key has a special purpose - it is mathematically needed to create valid transactions that spend the funds originally sent to the address. If the private key to an address is lost (for example, in a hard drive crash, fire or other natural disaster), any associated Bitcoins are effectively lost forever.
Addresses can be created that require a combination of multiple private keys. Since these take advantage of newer features, they begin with the newer prefix of 3 instead of the older 1. These can be thought of as the equivalent of writing a check to two parties - "pay to the order of somebody AND somebody else" - where both parties must endorse the check in order to receive the funds.
The actual requirement (number of private keys needed, their corresponding public keys, etc.) that must be satisfied to spend the funds is decided in advance by the person generating this type of address, and once an address is created, the requirement cannot be changed without generating a new address.
What's in an address
Most Bitcoin addresses are 34 characters. They consist of random digits and uppercase and lowercase letters, with the exception that the uppercase letter "O", uppercase letter "I", lowercase letter "l", and the number "0" are never used to prevent visual ambiguity.
Some Bitcoin addresses can be shorter than 34 characters (as few as 27 in theory) and still be valid. A significant percentage of Bitcoin addresses are only 33 characters, and some addresses may be even shorter. Every Bitcoin address stands for a number - somewhat like an account number. These shorter addresses are valid simply because they stand for numbers that happen to start with zeroes, and when the zeroes are omitted, the encoded address gets shorter.
Several of the characters inside a Bitcoin address are used as a checksum so that typographical errors can be automatically found and rejected. The checksum also allows Bitcoin software to confirm that a 33-character (or shorter) address is in fact valid and isn't simply an address with a missing character.