I agree with the other answers that it's best called a finger joint or maybe a finger jointed corner brace .
You could also call it a box joint if you want to distinguish it from the tapered finger joints that are sometimes used to join boards end-to-end in stock made up of shorter pieces.
The point of a corner brace is to add support to the corner joint.
Usually, the brace is connected to each rail with glue and screws.
Using a finger joint here adds a lot of glue area in a shearing direction, so the connection between brace and rails should be very strong even without mechanical fasteners.
Forming that joint in a production setting would be fast and cheap, and it would save the cost of maybe 16 screws per chair and the time needed to drive them.
I found another example at dutchcrafters.com , which describes these braces as "grooved":
woodworking.stackexchange.com/users/492/Caleb
While the corner brace is pretty common in chairs I've never seen what appears to be a 'finger' joint incorporated with it.
But that is the best I can guess, a finger joint for the brace.
woodworking.stackexchange.com/users/27/bowlturner
This looks to be some sort of Finger joint, probably used as an Assembly joint to make it easier to assemble.
You could apply glue to the corner brace, then run a screw through it, and not have to worry about clamping it while the glue dries.
woodworking.stackexchange.com/users/286/LeeG
There is no official name for many more complex types of joints, and once you get to combining different types of joint techniques you can only really do your best to describe them succinctly.
There's a really great woodworking glossary website here: http://www.hobbithouseinc.com/personal/woodpics/_g_A.htm which describes lots of types of joint, but even he gets to the point where he's calling things something like an "angled keyed dovetail half lap joint".
It is probably the most accurate way to describe the particular joint he's talking about (roughly half way down the page) but there's not a single person who, if asked to joint two pieces of timber using an angled keyed dovetail half lap joint, wouldn't ask you to explain with a drawing.
"Interlocking corner brace", "finger jointed corner brace", "
box jointed angle brace" and "grooved corner brace"
all seem like reasonable names for the joint to me.
woodworking.stackexchange.com/users/272/WhatEvil
Interlocking corner brace.
I only found one company that uses it.
woodworking.stackexchange.com/users/523/Raymond Kornele
I removed the seats from dining chairs I just bought but have never seen this type of construction. What is it called?
What is the name of the corner joint with grooves on this chair?
woodworking.stackexchange.com
<joinery><furniture>
woodworking.stackexchange.com/questions/1230
woodworking.stackexchange.com/users/513/Kat
The joint in question is known as a Finger Joint, interlocking corner brace or box joint. The joint in question is a sort of finger joint  or maybe a  finger jointed corner brace, possibly used as an assembly joint. It has also been described as an interlocking corner brace or a box joint.
It is a sort of finger joint  or maybe a  finger jointed corner brace, possibly used as an assembly joint.  Interlocking corner brace. Box joint.