The "use" is crossbreeding trees. Forestry has like 20 different trees in it that you can only get via this method.
You need to get a sapling drop from the changed leaf block. Usually the chance is really low, but if you use a grafter (a tool from Forestry) then you can get 100% sapling drop rate. Note that it works only on trees with Forestry's genetic data! So vanilla trees won't react to the grafter (unless you run them through a treealyzer or a multifarm before planting to convert them to Forestry), and neither will for example silverwood trees from Thaumcraft. Changed leaves always count as having a genome, so the grafter always works on them.
The sapling you get will (usually) in 90% of all cases be a combination of the traits of the parent trees, and in 10% of the cases you'll get a mutation to a new tree species instead. Just like it works with bees.
The trees you can breed look fancy and have different wood colors for aesthetic building purposes, can grow nuts that give massive amounts of seed oil or fruit that give more fruit juice than apples, and can produce more saplings (or saplings that give more biomass in a fermenter than normal ones). They can also grow thicker and taller, giving you more wood.
By the way, wikis exist and help with such questions...