The mouthpiece of a woodwind instrument is the part which the player blows into.
On single-reed instruments like a clarinet or saxophone the mouthpiece is shaped like a wedge. The reed is placed near the player's bottom lip. This area is called the table. When the player blows, the reed vibrates. This is then made louder by the instrument.
The shape of the inside of the mouthpiece can change the sound very much. The sound made by a mouthpiece that is large and round will be very different from the sound made by a mouthpiece that is small and square.
The space between the end of the reed and the end of the mouthpiece is called the tip opening.
The facing (or lay) is the part of the reed that starts to curve around the end of the mouthpiece. The length of the facing can change the response of the instrument.
The ligature is what holds the reed onto the mouthpiece. Anything that can hold the reed onto the mouthpiece can be called a ligature. Most ligatures are made from metal or plastic. Some people like to use ordinary string to hold the reed onto the mouthpiece.