Ambergris is an excretion from the sperm whale that is found floating in the ocean or washed up on the beach. After floating in the ocean for years, the substance ages and turns into a material that has been a highly valued perfumery ingredient for centuries. It has an exalting effect on other ingredients in the blend, offering a sensual smoothing note that weaves between the levels in an interesting way. It can have notes of amber, incense, musk, animalics, and seawater. It is a rare and expensive ingredient because it is very hard to find the raw pieces. Ambergris pieces are shown in the picture (these are some pieces I purchased and photographed, photo is copyright Sonoma Scent Studio).
Amber and ambergris are not the same thing. Amber is an accord that is traditionally made from benzoin, vanilla, labdanum, and other ingredients such as woods and spices. Amber accords are sweet and vanillic, often with some brown sugary notes added. Amber accords can contain natural ingredients, such as labdanum and benzoin, and synthetic ingredients, such as Ambroxan and Cedramber.
To make things more confusing, Ambroxan is a synthetically derived aroma chemical that is one of the aroma chemicals naturally found in ambergris. Sometimes when you see ambergris listed as a note, the perfumer may mean a synthetic approximation such as Ambroxan. Natural ambergris is rarely used in commercial scents today.