Reading the book, I couldn't find anything obvious about martyrweed's uses in that first mention of it.
As Morrigan said in a comment, it might be some sort of all-natural voice stress analysis system. Indeed something like that was my first thought - something about the plant "listening".
Reading it again though, it might instead be that martyrweed can muffle sound – providing security in the sense of privacy.
In the scene you mention, Kovacs finds Laurens Bancroft in a conservatory with glass walls, yet the room is described as a "sound absorbent environment" - possibly because of the martyrweed Bancroft is tending to there.
Later, Kovacs runs into Miriam Bancroft:
In one hand she was carrying a trellised plant urn, held up like a lantern on a stormy night. Long strands of flowering martyrweed trailed from the trellis-work.
"Have you–" she started.
I stepped closer to her, inside the range of the martyrweed.
Emphasis added. In the scene, there's cause to be discreet, so again it might be that the plant is somehow absorbing sound, keeping conversations, well, hush-hush. The scene could be construed as Miriam deliberately carrying the plant with her in order to have a private conversation with Kovacs.
The final mentions of martyrweed (much later in the book) are the most direct descriptions of its effects, and it does indeed seem to be about sound absorption:
The bitter echoes of her voice were leached out of the room by the martyrweed. The silence thickened.
The only scenes the plant appear in are those where people are having sensitive conversations. And it's only seen at the Bancroft residence, which is plenty physically secure already. But if its uses are about privacy and sound dampening, it'd fit with the sort of court intrigue, the-walls-have-ears mood of the Bancroft household.
Regardless, while the uses of martyrweed may be obvious to Kovacs, I wouldn't say they're ever made terribly obvious to the reader.