On your Magento website your products can be searched for by their attributes, these may be name, description, size etc etc but you may want to increase this or make a new brand new attribute searchable
For this example we will assume that you want to make the attribute "colour" searchable. It may be very beneficial for your customers to be able to search for "Pink" and all of the pink products are viewable.
All you need to do to allow this is log into your Magento admin panel, and then go Catalog - Attributes - Manage Attributes
From this menu you can select an attribute and choose using "Use In Search Results" if the attribute is searchable.