The full explanation is on the jump, but basically the UAV goes out the trash tube in a canister, floats to the surface and launches.
The two big questions that instantly pop to my mind are 1) Where did that UAV come from? and 2) How do they intend to recover it?
Raytheon's caption for the submarine-launched UAV graphic:
(fig. 1) A significant mass is added to the SOTHOC submarine launch vehicle to allow safe separation from the submarine when it is ejected from the TDU (Trash Disposal Unit); (fig. 2) the center of buoyancy and center of gravity of the SLV are offset along the longitudinal axis; after the SLV separates from the submarine, it revolves around the center of buoyancy and begins to shed the deployment weights; the SLV then travels unconstrained to the programmed maximum depth before returning to the surface; (fig. 3) a float collar adds buoyancy to bring unit to surface; (fig. 4) a wind vane deploys; (fig. 5) the water drogue assures stabilization at the surface; (fig. 6) wind vane helps adjust tube direction as required, the launch tube pivots to a 35-degree angle for UAS launching.