A muddler is a rod with a flattened end (similar to a pestle) that is used to mash or crush cocktail ingredients. For example, it can be used simply to crush ice for any cocktail, or to mash together mint and sugar syrup for Mint Julep, or lime quarters and sugar for a Caipirinha.
Muddlers are typically made from wood and range in size from 12-25 cm in length; make sure that you choose one that is long enough for the equipment that you are using.