"Linings" or "kerfing" provide a platform for gluing the top and back to the sides. The extra depth also allows the builder to route a channel for the exterior "bindings" without cutting off the top or back.
Laminated linings are stronger and more rigid than kerfed linings with no significant weight gain. Pictured are the sides of Ebi Tenor Ukuleles number 16 and 15. Strong and rigid sides provide a superior tonal base for the top and increased durability for the instrument.
Traditional kerfed linings look like this. These linings form a sufficient platform for gluing on backs and tops, but due to the kerfs, add little to the strength and rigidity of the sides.
"Reversed kerfing" (not shown) does add some strength and rigidity to the sides, but not as much laminated linings.