How does the debris rejection system in the CFM LEAP engines work?
It's an inertial particle separator system incorporated into the compressor inlet.  It forces intake air to follow a curved passage that makes particles with mass sling to the outside of the duct due to the sudden change of direction, where, when required, those bypass ducts open into the stream to dump the particle laden air overboard.  

Turboprops have used inertial particle separators that can be opened or closed for eons; this is the first time I've seen the concept applied to a jet.  It's desirable for turbojets and turbofans to have an inlet that's good at "catching" air for a good ram effect; better for efficiency and a strong ram effect makes the engine windmill well (important for re-light capability).  Problem is, strong ram effect also means a lot of particles being ingested.  While large objects like birds are an obvious factor, with jet engines there is actually a more subtle long term problem, sand particle ingestion that literally sandblasts the compressor blades over time and shortens the life of the engine.  This is a huge problem in desert operating environments.

Some engines like early versions of the GE CF-34 used a compressor inlet profile that was "flush" to the airflow downstream of the fan, which tended to encourage particles to pass on by in the fan discharge. This was a design goal for the A-10 Warthog, for which the engine was originally designed, and made it fairly FOD resistant.  Similar variants were used in the Challenger business jet and the CRJ200 Regional Jet.  

Problem was the ram effect was low, which made it windmill poorly (you have to maintain a fairly high speed if it flames out, to keep the core of the engine from stopping - the dreaded "corelock").  On later commercial variants, the compressor inlet profile was revised to present a more direct into-the-flow inlet for the compressor, improving efficiency and making the engine able to windmill at low speeds.  The price of this was the FOD resistance was reduced and in sandy environments the erosion wear problems went way up.

This design appears to be an attempt to keep a compressor inlet profile with a good ram effect while providing the ability to minimize sand ingestion when required.  The benefit is decent engine life for operators in sandy environments.  Middle eastern airlines would be very keen to have this feature because they tend to suffer from short TBOs from their engines getting sandblasted.