Class TestHolder needs to call the private constructor in Test. But it's private, and can't actually be called from another class. So the compiler plays a trick. It adds a new non-private constructor to Test which only it knows about! That constructor takes an (unused) instance of this anonymous class Test$1 -- which nobody knows exists. Then TestHolder creates an instance of Test$1 and calls that constructor, which is accessible (it's default-protected.)
You can use javap -c Test (and javap -c Test\$1, and javap -c Test\$TestHolder) to see the code. It's quite clever, actually!