My 2c:

The goal is longer, thinner wings than usual. Long and thin wings are far more efficient—think gliders and the U2. But beyond a certain width, those wings become incompatible with existing airports and other facilities for handling commercial aircraft. So the idea is to mount folding extensions that are extended for flight, but likely fold when being hangered or navigating taxiways.

Ground infrastructure.

E.g. for the 777X it fits in Category E. Without folding tips it would be in Category F. Less gates can accommodate Category F.

https://skybrary.aero/articles/icao-aerodrome-reference-code

> The Wing of Tomorrow programme is centred around creating longer, lighter, and more slender wings to maximise aerodynamic efficiency and reduce fuel burn. The wing extensions will be assembled at Airbus’ Wing Technology Development Centre in the UK and flight tested in Toulouse.

An airliner weighs a certain amount. In cruising flight, the lift on the aircraft is exactly equal to the weight (because it's neither climbing nor descending). Aerodynamic drag falls into 3 buckets: parasitic drag, wave drag, and lift-induced drag. Lift-induced drag is drag created by the wings producing lift.

Longer, thinner wings (higher aspect ratios) create less lift-induced drag for a given wing area, so ideally you want a super duper long and skinny wing, which will create less drag for a given amount of lift, and thus improve your fuel efficiency. Fuel is a massive portion of the total cost of operating an airliner, so there is a large financial incentive from the airlines to reduce fuel costs.

Unfortunately really long wings make airliners too wide to park at most airport gates, and in some cases too wide to taxi safely around obstacles, so they're experimenting with ways to make the wings fold and get a "best of both worlds" situation.

Operation from aircraft carriers, obviously. /s