The tunnel was designed by London's then chief civil engineer Sir Alexander Binnie opened in 1902. It is is 1,217 feet long and is about 50 feet below the Thames.
Originally built to get South Londoners who worked in the docks North of the river to work, it has largely been superceded by the DLR which now transfers bankers to their jobs in the same areas.
Clearly, it's just a tunnel and isn't worth making the journey in itself, but if you're down that way why not get off the DLR a stop early and have a look. It is also handy for cyclists to cross the river, and is part of the UK's National Cycle Route 1 which links Inverness and Dover. However, you must push bikes through the tunnel and the lift isn't always working.
The best DLR stops are Island Gardens and Cutty Sark for Maritime Greenwich. For more information see the page on Wikipedia.