Honestly, there isn't a whole lot to say about splines that can't be gleaned from the left 2 images, but I figure they are worth covering.
Splines are thinner pieces of wood set into a cabinet, often on the corners of two adjoining pieces of wood. They are glued into cut grooves and offer extra support to a joint. They provide extra support because they add extra long grain glue surface to an end grain joint. If you've missed my other posts, end grain absorbs glue and leaves a weak and worthless joint on its own. Long grain glue joints are often stronger than the wood, so most joinery is concerned with increasing long grain glue surfaces.
Splines area great reinforcement for miter joints. They can be thin or thick. Unlike hidden joinery, splines can be used as an aesthetic element as well. They are often found in contrasting woods to the main cabinet structure. Though using the same wood for splines as the cabinet, provides a nice subtle detail that doesn't scream for attention.