Faucet Packing and Washers
Compression faucets rely upon rubber or nylon washers and a seal around the faucet stem. Older faucet designs use a graphite or waxy coated thick twine-like string around the top of the stem. Newer models use either a rubber washer inside the stem-retaining nut or O-rings.
Replacing the O-ring(s) or washer is easy, just remove and take to your hardware store to find the exact replacement.
For faucets that use packing, just remove the old faucet packing string and any residue from the stem. Then tightly wrap the new faucet packing around the stem. Trim any remaining excess packing string and just put the faucet back together.