What Does a Ligature Do?
A ligature holds a reed onto a mouthpiece. Saxophones and clarinets use ligatures. The reed must be secured firmly by a ligature against the table of the mouthpiece to make it vibrate freely. Ligatures are usually made of metal plated in nickel, gold, and silver. Most ligatures are tightened by one or two screws. It is important that your ligature fits perfectly with your mouthpiece.
Most instruments come with a basic metal ligature. Reeds cannot vibrate properly without the ligature to hold it securely against the mouthpiece. The vibrations they make will result in easier, cleaner, and faster notes to articulate. This basic ligature will last for a while but it'll eventually warp or break. When it's time to replace the ligature, you might want to consider upgrading to a better one.
Some finer, step-up instruments come with ligatures that are poorly made. This is because the manufacturer knows that the musician has already invested in an upgraded ligature that they prefer. More often, the musician will have already played and own several ligatures that they use depending on the type of sound they want to produce.
Players can have multiple ligatures because they use them for different situations and types of music. Your choice in ligature will depend on the type of sound you want. Just like your reeds, the only person that can tell you what type of ligature will work best is yourself.