Dog Ear Terminology
Of course a dog's ear consists of all the anatomical structures that faciliate hearing. But for dog judges, breeders and fanciers, the ear leather (also sometimes called the lobe) is of prime importance. The ear leather varies enormously from breed to breed in size, shape, thickness, carriage and mobility. The 'set on' or where the ear is attached to the skull is also important. All these factors tend to be characteristic of individual breeds, and hence have a great influence on both ‘expression’ and breed type.
Each ear leather consists of cartilage, covered on both sides by skin, the outer side of which is covered with fur and the inner side smooth. The point of junction of the ear leather to the head is called the ‘set on’[Ref 1].
Pricked or Erect Ears
The small, thick textured ears of the Samoyed are 'set on' high and covered with dense hair and set well apart on the skull. There they are protected from the cold by the thickness of the lobe itself as well as by the thick dense coat that covers them. 
The German Shepherd Dog on the other hand was bred to work in more temperate conditions so the texture or thickness of the leather itself and the coat that covers them is not as critical as the ears of the Samoyed. So whereby German Shepherd ears are also pricked or erect, they are larger than the Samoyed's, and even 'set on' higher and closer together on the head.
Semi-Erect Ears
This refers to a basically erect ear, with a 'set on' high on the head like ear of the German Shepherd Dog, but with the top third tipping forward. In the case of young puppies of some breeds, potentially erect ears can be semi-erect until the teething process is complete.
Button Ears
Button ears also are 'set on' high like the erect or semi-erect ear, but more than half the ear is folded. This causes the ear to sit well above the level of the skull, with the tips pointing towards the eyes. The leather of the ear then covers the orifice, protecting it from the earth of the tunnels in which the terrier was originally bred to hunt.
Side Placement Ears
On this Airedale Terrier, these ears also serve the purpose of protecting the orifice of the ear from dirt, somewhat like the button ear. Although still 'set on' high, with side placement ears the leathers are usually physically larger and thicker than button ears and should point towards the ground. For the purpose of illustration, on the Airedale pictured the ears should correctly be carried above the level of the skull because they are set on high. But in most other breeds where side placement ears are required, the 'set on' is lower, either level with the skull (Parson Russell Terrier) or below the level of the skull.
Rose-shaped Ears
These have small relatively thin leathers which fold backwards, so you can see the inside of the ear or the burr. In the Staffordshire Bull Terrier and Bulldog, the rose-shaped leathers are 'set on' high but at the back of the head. Historically this type of ear served the purpose of protecting the leather of the ear from damage by its opponents. Today, this rose shaped ear adds to the dog's soft expression, complemented by its round eye.
In the case of the Whippet and other Sight Hounds that were bred to run at high speed in a double suspension gallop, in this type of ear they are set on low, as by folding backwards when the dog is galloping, they serve the purpose of 'streamlining' the dog.
Dropped Ears
Dropped ears hang straight down from the head and are therefore 'set on' low on the skull unlike those above. There can be a small amount of lift at the back of the ear, but it should never fold above the level of the skull. Sometimes also called a pendulous ear, a dropped ear is the opposite of an erect ear both in the size of the ear lobe and the low 'set on'.
References and further reading:
[Ref 1] Harold R Spira “Canine Terminology” Harper & Row Sydney 1982 Pages 43 - 49