Samphire is a type of seaweed, gathered on the Norfolk coast amongst other places. It can be cooked (like cabbage) and is apparently delicious! It is mentioned in King Lear Act IV Scene vi.
The samphire served as a delicacy, Salicornia europaea, is found in East Anglia, Lancashire and other coastal areas. It is a marshland herb and is usually cooked lightly, like asparagus, and served with butter or Sauce Hollandaise.
The one mentioned in Shakespear is Crithmum maritinum, or Rock Samphire, which grows on cliffs and shingle beaches on the south coast of Britain. It is not normally eaten nowadays but was used to flavour pickles in Shakespear's time.