Oils are liquid fats. They are derived from plant sources (seeds, nuts, that sort of thing) and like animal fats have been in use by human beings for thousands of years. Speaking generally, they’re used more by cooks than bakers — solid fats are where it’s at for pastry types — but come in quite handy from time to time.
In the pastry kitchen oils are most valuable when they bring little-to-no flavor to the party. Though a walnut or a sesame oil might occasionally be used specifically for its flavor, most of the time pastry makers use oil solely to introduce richness and/or a moist texture into a cake or muffin formula. The same goes for frying, where the aroma of, say, peanuts or corn can muddle the profile of a fritter or a doughnut.
So the oils most commonly found in the pastry kitchen are neutral-tasting: vegetable (made from soybeans) and Canola (made from pressed rapeseed or mustard seeds). If they’re neutral in flavor and have a high smoke point, so much the better. As it happens vegetable oil has a smoke point of around 370 degrees Fahrenheit and Canola can take heat up to about 435. Gotta love those Canadians.
Other useful oils include corn oil (if you make a lot of corn bread) or olive oil which, even though it has a very distinctive flavor, is very nice for little Italian cakes. Olive oil is also rich in emulsifiers, and that can be extremely handy when you want to produce a cake with a very fine crumb.
Of course the word of pastry is wide, and the potential applications for oils of all types are legion. But I’m a simple man with simple needs. Give me a nice big jug of Canola oil and, for the most part, I’m good.