$BTC

Broadcasting and confirmations

In the above example, Mark (via his wallet software) will broadcast his proposed transaction to the Bitcoin network. A special group of participants in the network known as 'miners' verify that Mark's keys are able to access the inputs (i.e. the address(s)) from where he previously received the bitcoin he claims to control. Miners also gather together a list of other transactions that were broadcast to the network around the same time as Mark's and form them into a block. Any miner who has completed the 'Proof of Work' is permitted to propose a new block that will be added or 'attached' to the chain and by referencing the last block. That new block is then broadcast to the network. If other network participants (nodes) agree it's a valid block (ie. the transactions it contains follows all the rules of the protocol and it properly references the previous block), they will pass it along. Eventually, another miner will build on top of it by referencing it as the previous block when proposing the next block. Any transactions that were in the previous block will now have been 'confirmed' by the next miner. As blocks are added to the chain, the number of confirmations of Mark's transaction increases.

Why do some bitcoin transaction confirmations take so long?

Each block can only contain a certain number of transactions, and that number is determined largely by the space available in each block, or the 'block size,' which is 1MB. The limited space gives rise to the fee market, where miners, who collect fees, choose to include in the next block only those transactions which have included a high enough fee. Thus higher fees act as incentive for miners to prioritize your transactions.

Note that the block size is an arbitrary limit, but the Bitcoin community has chosen to keep the block size as small as possible in order to make it easier for people to operate Bitcoin nodes. Bitcoin Cash, which is a fork of Bitcoin, has a larger block size and therefore requires much lower fees for transactions.