What is a 6.3mm plug adapter?

This adapter is also called a TRS adapter,phone jack adapter or a 1/4" adapter among many other names.

The 6.3mm jack, originally called the TRS connector was invented for use in telephone switchboards in the 20th century and is still widely used in its original ¼″ (exactly 6.35 mm) size.

An adapter would connect another type of plug to the TRS plug (male or female depending on the situation.