An ocarina (pronouced "ah-kah-ree-nah" ...That clip is totally stolen from Merriam-Webster.com) is a wind instrument, usually shaped like an oval, with finger holes and a potruding mouthpiece. The type of ocarina Link uses is called a Sweet Potato Ocarina. As the name suggests, these ocarinas are made out of sweet potatos, which gives them their elongated shape. Other common types of ocarinas are clay ocarinas, which are usually spherical but can be made into any shape imagineable.
The ocarina is one of the oldest instruments, dating back to ancient civilizations. They can be found on several different continents and can be made from most anything including antlers, bone, precious stones like quartz, and even seaweed. Early ocarinas were often shaped like animals and used to imitate bird calls. Many cultures also thought the ocarina to have magical qualities and used them in ceremonies. The modern ocarina was invented by an Italian teenager by the name of Guiseppe Donati in 1853.
In Ocarina of Time and Majora's Mask, the ocarina is portrayed as having magical abilities. The songs Link plays are capable of manipulating many things, from the weather to time itself. The ocarinas Link receives hold sentimental value as well, having been trusted to him by his best friend Saria and Hyrule's princess, Zelda.
Inarguably one of the most important items Link uses on his quest, the ocarina stays true to its cultural and mystic roots, serving as a magical aid throughout Link's journey.