The mortar is a bowl-like vessel used to contain the substance to be ground. Mortars have smooth, rounded bottoms and wide mouths. The pestle is the pounding and grinding instrument. The mortar and pestle are usually made of wood. Inexpensive ones may be plastic, but this does not work very well. More expensive ones may be made of stone or porcelain, perhaps with a wooden handle. Wooden mortar and pestle sets should only be used with dry food, such as dried spices.
To grind spices, you should normally apply a decent amount of force in a way that causes the spices to get dragged under the sideways-moving pestle. Create a fine powder to help the spices release flavor. A bit of salt, commonly needed in a recipe anyway, will make this work much better. After you have emptied out the spices, a wooden mortar-and-pestle set should be cleaned by grinding some plain salt. (you may discard the salt if you wish). Do not wash a wooden set.
The Mexican version of this set of tools is the Molcajete y Tejolote (from Nahuatl, literally "sauce bowl" and "stone doll"), which are often made of basalt, giving them a rough finish and dark grey or black color. They are well-suited to grinding wet ingredients such as tomatillos and avocados.