Road Closure Requests are a new type of Map Problem that are automatically imported into the editor from Elgin. Here's what you should do with them...
First, attempt to verify if they are valid, and maybe get some more accurate details about the location, direction and duration. The reports from Elgin (also Roadworks.org.uk) are mostly spot on, although often claim the closure is for an entire day rather than just working hours.

If the closure request is bogus, for example on a cul-de-sac, non-drivable road or lane closure, then mark it as Irrelevant data. This feedback will be passed back to the feed provider so they can improve their information.

If you have necessary permissions to set closures on the relevant segments, then go ahead and set the closure. If you don't have permissions, then you can pass the request up to a higher editor to implement for you, as per this thread. Remember to include all the information needed to set the closure.

Further tips:

• The UR/MP Tracker extension can show you all the closure requests in your area.
• If the segment needs splitting, and the closure starts more than a week in the future, you can probably get away with it as long as you remember to come back after the map has updated.
  Otherwise, you'll have to figure out which segments are best to close.
• Daytime or overnight closures that repeat over several days are easier to apply via the Closures sheet.

Addendum: Requests from TrafficMaster will no longer appear in WME.