Seoi Otoshi is very similar to Tai Otoshi. The only apparent difference to a casual observation is that the leg upon which Uke falls over is behind Uke's own leg instead of in front of it.
In this demonstration, note how Tori is moving as if into Morete Seoi Nage (two handed shoulder throw) whereupon Uke resists by going Jigotai. With that Tori sweeps his leg around and behind his opponents leg and whilst pulling forward with his hands also snaps his trailing leg straight which has the effect of catapulting Uke upwards. This throw is a very decisive one. If it works, it will usually result in a major score.
Note: This version of Seoi Otoshi is as specified in the BJC syllabus. It should be noted that it differs from the Kodakan who call this throw 'Seoi Nage'. The throw that the Kodakan refer to as Seoi Otoshi involves dropping down onto one or both knees but is otherwise similar. The BJC (and Chalfont Judokwai) do not encourage dropping onto ones knees because of the consequent damage to the knee joints that occurs over time if done regularly.
Here you can see the key components of this throw frame by frame: