Ligatures hold your reed and mouthpiece together and onto the instrument. Early on, ligatures were made of twine that was wrapped and tied over the reed. Today, ligatures are made of metal and they're carefully crafted to fit securely and be adjusted if necessary. Even today's caps are well-designed and made of flexible materials, so they won't break or chip.
If you're searching for a new ligature or cap, you'll find a huge selection at Woodwind & Brasswind. There are ligature and caps to fit every player's price range from respected manufactures like BG ligatures, Vandoren, Rovner, Yamaha, Theo Wanne and countless others. The right one for you will depend on the instrument you play, how much you're willing to spend and what you like from a look & feel standpoint.