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This Vacuum Hose Fitting Adapter is used to attach a 1" inside diameter vacuum hose to 3M™ Random Orbital Sanders.
On one end, it has a 1" vacuum hose external thread (left hand thread), which screws into the random orbital sander exhaust assembly.
On the other end, it has a 1" friction fit barb that pushes into the inside of a 1" vacuum hose.
In practice, this adapter is commonly used to connect the sander to a 1" piece of hose, such as the MMM 28301 (cut to length), and then using an appropriately sized push-on adapter, connecting to the hose of your central or cannister vacuum.
See Related Products, below.
Heavy on the technical side...
While, in theory, you could dispense with this adapter by screwing the externally threaded hose directly in the sander exhaust, in practice, this is quite inconvenient, as you'd have to spin the hose or sander around.