The Barnett formula is the formula used by the government to allocate funds to the devolved assemblies. It works by starting with a budget change in an English department, considers how comparable the services provided by the department are to those provided by the devolved administration, and applies a population proportion. This provides a figure to determine a budget allocation to the devolved authourity.
The Barnett Formula is not set out in law, and there is wide government discretion as to how it should be applied. As a result of the DUP Coalition deal, which provided for greater spending for Northern Ireland, this promise has come under scrutiny. However, GovTracker continues to give this promise a 'kept' status because the Barnett Formula continues to be implemented in its pre-election format. This is because the 1 billion pounds granted to Northern Ireland comes as an extension to their block grant. This is a similar grant to the ones given in city-deals. For example, Glasgow received 500 million pounds in it's deal. These deals do not factor in the Barnett Formula consequentials. This means that the Formula has been kept in place, despite accusations of over-spending in Northern Ireland. Full Fact have produced a useful explainer - https://fullfact.org/economy/northern-ireland-and-barnett-formula/.
Source: Manifesto - Page 31
Reference 1: Treasury Report
Reference 2: BBC Article