A formal acknowledgement on the part of an Other, that they won’t interfere with mankind without excuse, they’ll obey certain rules, and the practitioners will leave them be. Typically an Other bears some symbol or token of this bargain. Over time it’s gained a power of its own and being sealed physically alters the Other, but it also affords them certain protections against practitioners. Like restrictions against lying, similar to practioners.
While most of the older Others are affected by this, many of the newer ones aren't and can act without it interfering with them, however the universe itself conspires to protect the innocent humans as a result. An Other who isn't bound by the seal and also elect to be bound by it to have a greater significance in the scope of things and a power source, but it will open them up to more ways of being sealed and handled as a result.
In addition a bogeyman bound by it would make them easier to keep track of and form deals with. It would nail them down in shape, form, and demeanor, stopping the Abyss from getting as much traction with them. It allows them to maintain the balance of Other and Human within.
In the case of Blake it could quite possibly slow down the rate at which the rift between him and Rose widened due to their origins.
↑Given Barbatorem’s nature, this author would recommend another means of baiting him in the future, as he will remember, anticipate and adapt with each means used. He agreed to be bound by the seal of Suleiman bin Daoud four months after the initial capture. See the Others volumes, book one, chapter one, if unfamiliar with the seal. The diagram this author used for entrapment, necessitating only one line to open or close, can be found on page five of this entry, followed by the means of summoning and the recommended diagram for imprisonment. - Bonds 1.7
↑“Challenging me? Prove it, then,” he said. “The Barber is sworn to the Seal of Solomon. Johannes is a practitioner. If you would mark us as liars with a meaningful show of faith, we’ll be disadvantaged.” - Judgement 16.10
↑Mags: There are options, Blake. The seal of Solomon, if you were willing, would mean giving up some control, but it helps others control your impulses. - Execution 13.4
↑“You’re an Other,” Maggie said. “That place is like an Other’s amusement park. There, it’s like the old days, before the Seal of Solomon. Before humans were really able to fend for themselves.” - Damages 2.2