Limey Lurker,
Yep, and I'm also "initiated". Have a look at a good text book and you will see for example if you have a 8" x 2" floor joists and you want to insert a 'hole' to accommodate a stairway you will find that you will need to cut some of the aforesaid floor joists for that and you will have to support those 'cut' ends.
So, what you then do to support that is to introduce an 8" x 3" joist (the trimmer) between the 'uncut joists on either side of the opening either by A) using a tusk tenon or B) using a joist hanger and then support the ends of the previously cut 8" x 2" joists (the trimmed joists) using either methods A or B to the trimmer.
And in the context of the OP, if that no-load bearing brick wall *was* resting on top of a trimmer joist, then that will more than carry the weight - as will the standard joists
Bloody hell, now it's time for a cuppa! :-)
Cash