It is a very specific reinforced rubber hose, which apparently dry rotted enough to tear. It is the flex line that supplies hydraulic pressure to the wheel cylinder from the master cylinder. You will need to bleed the entire system now (master cylinder included as I will wager over the past 48 hours I have seen this thread all of the brake fluid has drained out of the system.
You will need an old Chiltons, or a newer Haynes manual to show the step by step procedures they are more general (covering all makes and models generically). The service manual, which is more specific in detail by model, assumes you are a service technician and know what to do when it says R&R a part. The service manuals, Fisher Body assembly manual, and electrical wiring manuals are all available as reprints on CD; or you can search for a real paper version which appear occasionally and can be had from e-Bay (both cost money, can not remember how much the CD is).
You may get by with the drum brakes on the front so long as it is a six cylinder vehicle but if you improve the vehicles performance, you need to seriously consider improving the brakes as well. I and most others recommend disc brakes on the front (stock 11" disc work fine 12" is as an upgrade off a Camaro) and at least 11"x2" drums in the rear (9"x1-3/4" is stock) available for sale as a complete kit in the back of most car mags.
Drum brakes are pretty universal in their installation and maintenance, and GM is prone to use parts off different vehicles to improve performance (the 11" rear drum brake upgrades are considered standard brake parts off of a Caprice Estate Wagon).
Single caliper disc brakes were standard on all high performance cars by 1969, and there are many donor vehicles to obtain parts from in wrecking yards. I would recommend getting a copy of ADP Hollander's Nova reprint book (about $40) to determine who is a good candidate for what parts. Most yards only have newer vehicles (seven years old is ancient in the recycler's mind) and if you call them asking about a thirty five year old part they will not likely be able to help you unless you can ask if they have a certain Hollander number in stock.
Big Dave