Any computer that connects to the Bitcoin network is called a node. Nodes that fully enforce all of the rules of Bitcoin are called full nodes. Most nodes on the network are lightweight nodes instead of full nodes, but full nodes form the backbone of the network.
What makes a full node?
Full nodes download every block and transaction and check them against Bitcoin's core consensus rules. Here are examples of consensus rules, though there are many more:
- Blocks may only create a certain number of bitcoins. (Currently 25 BTC per block.)
- Transactions must have correct signatures for the bitcoins being spent.
- Transactions/blocks must be in the correct data format.
- Within a single block chain, a transaction output cannot be double-spent.
If a transaction or block violates the consensus rules, then it is absolutely rejected, even if every other node on the network thinks that it is valid. This is one of the most important characteristics of full nodes: they do what's right no matter what. For full nodes, miners actually have fairly limited power: they can only reorder or remove transactions, and only by expending a lot of computing power. A powerful miner is able to execute some serious attacks, but because full nodes rely on miners only for a few things, miners could not completely change or destroy Bitcoin.
Nodes that have different consensus rules are actually using two different networks/currencies. Changing any of the consensus rules requires a hard fork, which can be thought of as creating a new currency and having everyone move to it. Consensus rules are different from policy rules, which specify how a node or miner prioritizes or discourages certain things. Policy rules can be changed freely, and different nodes can have different policy rules. Because all full nodes must use exactly the same consensus rules in order to remain compatible with each other, even duplicating bugs and oddities in the original consensus rules, creating a full node from scratch is extremely difficult and dangerous. It is therefore recommended that everyone who wishes to run a full node use software based on the reference client, which is the only client guaranteed to behave correctly.
At minimum, a full node must download every transaction that has ever taken place, all new transactions, and all block headers and Merkle trees. Additionally, full nodes must store information about every unspent transaction output until it is spent. Modern-day full nodes are inefficient in that they download each new transaction at least twice, and they store the entire block chain (>30 GB) forever, even though only the unspent transaction outputs (<1 GB) are required.
Why should you run a full node?
Full nodes form the backbone of the network. If everyone used lightweight nodes, Bitcoin could not exist.
Full nodes provide various services to other network participants. This is especially important for lightweight nodes.
These services include:
- Filtering transactions and blocks on behalf of lightweight nodes so that lightweight nodes do not need to download every transaction ever made on the network in order to find their own transactions.
- Serving historical full blocks to nodes that have been offline for a while.
- Transmitting new transactions from users to miners.
- Broadcasting new blocks from miners to other nodes.
For the most part, these services are only usefully performed by full nodes that are listening on port 8333. Other full nodes and all lightweight nodes are actually a slight drain on the network's resources. The more full nodes that accept incoming connections there are, the more users the Bitcoin network can support.
This is by far the most important reason for running a full node, though it is a little difficult to understand.
As explained previously, full nodes enforce the consensus rules no matter what. However, lightweight nodes do not do this. Lightweight nodes do whatever the majority of mining power says. Therefore, if most of the miners got together to increase their block reward, for example, lightweight nodes would blindly go along with it. If this ever happened, the network would split such that lightweight nodes and full nodes would end up on separate networks, using separate currencies. People using lightweight nodes would be unable to transact with people using full nodes. If all businesses and many users are using full nodes, then this network split is not a critical problem because users of lightweight clients will quickly notice that they can't send or receive bitcoins to/from most of the people who they usually do business with, and so they'll stop using Bitcoin until the evil miners are overcome, which is the appropriate response. However, if almost everyone on the network is using lightweight nodes in this situation, then everyone would continue being able to transact with each other, and so Bitcoin could very well end up "hijacked" by evil miners.
In practice, miners are unlikely to attempt anything like the above scenario as long as full nodes are prevalent because they would lose a lot of money. But the incentives completely change if everyone uses lightweight nodes. In that case, miners definitely do have an incentive to change Bitcoin's rules in their favor. It is only reasonably secure to use a lightweight node because most of the Bitcoin economy uses full nodes.
Therefore, it is critical for Bitcoin's survival that the great majority of the Bitcoin economy be backed by full nodes, not lightweight nodes. This is especially important for Bitcoin businesses, which have more economic weight. To contribute to Bitcoin's economic strength, you must actually use a full node for your real transactions (or use a lightweight node connected to a full node that you personally control). Just running a full node on a server somewhere does not contribute to Bitcoin's economic strength.
Lightweight nodes are sometimes able to be temporarily tricked into accepting transactions or blocks that are not actually valid. This could cause serious financial damage, especially for websites that automatically process Bitcoin transactions. Full nodes provide the maximum security possible, and so they should be used by all businesses, and also by regular users whenever doing so is convenient.
Some are incentivizing it.
How to run a full node
If you run the Bitcoin Core/bitcoind wallet, you are running a full node. If you open port 8333, you will contribute to the network's capacity. If you actually use the wallet feature, or if you use a lightweight client like MultiBit but configure it to connect exclusively to your full node, then you will contribute to the network's economic strength and receive protection from some possible attacks against lightweight nodes.
There are a few alternate full node implementations, but they are not recommended for serious use because it is currently difficult to determine whether they implement the consensus rules with 100% accuracy. Even very slight inaccuracies could cause serious problems for the users of these alternate clients.