Symbolism, Imagery, Allegory
Sirius gives Harry two extremely useful gifts over the course of the novel (though Harry only opens the two-way mirror once Sirius has died and it's too late to be helpful). Harry does get a lot of use out of the knife that opens any lock. Sirius's joy in giving Harry presents – and the extremely useful nature of these gifts – shows exactly the problem that Sirius's character presents to the narrative arc of the novels as a whole.
Rowling has said that leaving Sirius alive would give Harry too much help on his road to facing Voldemort: "it is more satisfying I think for the reader if the hero [Harry] has to go on alone and to give him too much support [from Sirius] makes his job too easy, sorry" (source). It sounds cruel to say this, but Sirius's love for Harry appears to be why Rowling felt he had to die: too much help from a powerful adult wizard like Sirius would hamper Harry's ability to stand on his own two feet by Book 7.
These presents prove that Sirius is willing to assist Harry, possibly to the detriment of Harry's own character development. But as symbols of Sirius's love, they also draw out the tragedy of his death all the more. When Harry looks at the two-way mirror and cannot find him after Sirius has gone through the archway, we start to tear up a little. Sirius gave Harry these presents because he loves him, and now we have proof that that source of support has been brutally taken from Harry.