Consensus on the Tangle

In order to be useful as a payment network, IOTA must provide a method of knowing when a transaction can be safely considered to be confirmed. A confirmed transaction is accepted into the public consensus, and is very unlikely to be removed from it.
There are two approaches to establishing consensus in the tangle: the currently implemented coordinator, and the distributed approach suggested in the white paper.

The Coordinator

The coordinator is an entity controlled by the IOTA Foundation, which issues zero-valued transactions every two minutes, called a milestone. Using the coordinator, the definition of consensus is simple: any transaction referenced by a milestone is confirmed, and the others are not.

MCMC

The white paper suggests a distributed approach, which gives a probabilistic answer. This is similar to Bitcoin and other distributed ledgers, where at any given time a transaction has a confirmation confidence, which is an indication of its acceptance level.
In order to know the confirmation confidence for a particular transaction, we perform the tip selection algorithm 100 times, as described. We then measure how many of the 100 selected tips reference the transaction in question. If it is referenced by 80 tips of 100, for example, we say it is 80% confirmed.
The idea is the following: if it is very likely for a chosen tip to reference a transaction, then new transactions coming in will probably approve it. This effect will only increase with time, since the weighted walk causes large branches to grow and small branches to get abandoned.
The number 100 is arbitrary; if you need more accuracy, you may run the walk more times. Note that different nodes might see different confidence rates for the same transaction: this is because their view of the tangle is not identical, and their walks will reach different tips.