The signification of rending the garments is mourning, namely, on account of truth having been destroyed, or because there was no faith. We often read in the Word, especially the historic, of persons rending their garments; but the origin of this is not known at the present day, and it is also unknown that it was representative of grief on account of truth being lost. This act became representative from the fact that garments signified truths, as before shown (AC 4545) – From Bible

I don’t wish to challenge the interpretation above, but there’s a lesser significance to the rending of garments sometimes.  For instance, frustration over picking up 5 fouls in 10 ten minutes (video link culled from True Hoop)