Hazelnuts are considered a fruit. They are nuts, but the trees grow them and to the trees, they are fruit.
I read that nuts from all Hazel trees can be eaten.
Hazelnuts can be eaten plain. Mostly they are used to make sweets.
Hazelnuts are mashed into a smooth paste and can be spread on just about anything.
Hazelnuts can be whole or broken up and put in chocolate. They can also be used in cakes and cookies. The list is long on what can be done with this nut.
Coffee flavored with Hazelnut has a sweetish taste to it.

This first picture shows a nut sweeper. They wait until the nuts either all fall to the ground or the first bunch do and gather them up. The nuts get separated from the leaves, twigs and dirt. They get taken to where they are processed.

By, Sgtfarmer, English Wikipedia.

320px-Redsweeper Sgtfarmer en wikiAll the rest of the pictures are from Wikimedia Commons.

This is a hazelnut inside of its shell and husk  by, Andrzel Burak.

Haselnuss Andrzej Burak WCThis picture shows the hazelnut in its husk, shell and the fruit cut open  by, TonyTheTiger.

20130128_Hazelnut TonyTheTiger WCThe rest of the pictures were taken by H. Zell. This kind of hazelnut tree and fruit is called Corylus avellana.

Hazel tree.

Corylus_avellana_0001 H. Zell WCLeaf.

360px-Corylus_avellana_0009 H. Zell WCFlower.

360px-Corylus_avellana_0004 H. Zell WCA hazelnut tree bud.

360px-Corylus_avellana_0007 H. Zell WCHazelnuts growing on a tree.

320px-Corylus_avellana_0005 H. Zell WCHazelnuts in their shells.

Corylus_avellana_0008 H. Zell WCThis last picture is of hazelnuts with their shells removed.

Corylus_avellana_0006 H. Zell WC