The Wizards are in a tricky position cap-wise. With the money they're likely shelling out to keep Brad, Kuz and KP together, they'll need a lot cheap deals to round out the roster next year. Reggie Jackson, as an expiring deal, is a solid rental the Wizards can use for their playoff push and then let go. As a two-for-one deal, this move would allow them to sign Jordan Goodwin to a full roster spot for cheap.
The Clippers, meanwhile, have a star in Kawhi who wants an upgrade at PG. Monte Morris may not be the scoring threat Jackson is, but he has one of the best A/TO ratios in the league and shoots very well from the arc. He can be what they were hoping Wall would be. As a bonus, Gibson gives them some much needed depth at the 5.