This refers to S38 of the Highways Act 1980 (as amended) and is essentially a formal agreement for a highway authority to adopt (take over responsibility for) roads. This piece of legislation is most often used to adopt roads being built by another party (often a developer) and the agreement will include a set of drawings and sometimes a construction specification which the new roads are to be built to. It is usual for the other party to pay fees to enable the highway authority to check the works as they progress.
S38 agreements will normally contain a bond or cash deposit to cover the cost of the work in case the other party defaults in some way which allows the highway authority to step in and complete the works at no cost to the public purse. When the other party is a housing developer for example, then this protects the position of the individual house owner who may otherwise be liable for a share of the costs to complete the roads.