Regulation 25 transposes Article 25 of Directive 2014/24/EU on the treatment of economic operators based in GPA signatory countries or similar agreements the EU is party to. Albert has already split enough hairs about the small(ish) difference of the two texts: the Article refers to Annexes 1, 2, 4 and 5 of the GPA, whereas the Regulation mentions Annex 7 instead of 5. The reason for that difference is simply due to the coming into force of the 2011 GPA agreement in April 2014.
You should read Albert's entry for the GPA technicalities, as he puts his point across very well. I will focus my commentary on the "other agreements" part of the Regulation, particularly the forthcoming TTIP agreement between the EU and the USA as there is a chapter on public procurement market access open in the negotiations. If successful, these measures will open up the procurement markets in both sides of the Atlantic more widely than currently in the GPA.
Regulation 25 ensures that whatever conditions are offered in the TTIP to American economic operators, they will not be discriminated against when participating in public procurement procedures in England, Wales and Northern Ireland. For example, imagine that the TTIP includes financial thresholds that are identical to the ones contained in Directive 2014/24/EU which are slightly smaller than the GPA ones. American firms will thus be entitled to equal treatment up from that lower value contained in Directive 2014/24/EU.
The tradeoff offered by the TTIP is that European economic operators (including the ones based in England, Wales and Northern Ireland) will be entitled to similar beneficial access in American public procurement markets. As there are no language barriers between the countries and there is plenty of common legal ground between both jurisdictions, it is natural that UK, Ireland and the USA will see a higher degree of cross-Atlantic procurement than other Member States.
PS: On general TTIP issues check Dr. Paolo Vargiu's excellent blog.