Describe the use of pantaloon in The Taming of the Shrew.

I am going to assume that you are referring to
Pantalone* (a stock character from the Italian comic form
called Commedia del Arte).  Pantalone was a miserly old man
who was also a bit lecherous.  He often chased serving girls and tried to keep his
daughter from marrying.  He was also very stingy.

In
The Taming of the Shrew, Pantalone is analogous to
Gremio.  In Act II, Gremio shows how miserly he is as he
"battles" Tranio (disguised as Lucentio) in what he can offer Baptista for Bianca's
hand.

Baptista is often
considered as being derived from the Pantalone character too.  He spends much of the
play "duped" by Lucentio (disguised as Cambio), who is wooing Bianca behind his
back.

Many of the situations and characters in
The Taming of the Shrew are very close to Commedia, which was very
popular in Italy during Shakespeare's day.  And modern productions of the play often
reference the physical comedy and stock costumes of the Commedia in staging
Shrew.

*The
only use of the word pantaloon with which I am familiar
comes from pants/drawers and was coined in the 19th century, much after Shakespeare's
day.

For more on Pantalone, Commedia and The
Taming of the Shrew, please follow the links below.