OTHER NAMES Fairy Cake (in British), Patty Cake or Cup Cake (in Australian)
A Cupcake is a small cake designed to serve one person. It uses the same basic ingredient as standard-sized cakes, but baked in cupcake liners or aluminum cups. Just like large cakes, Cupcakes are decorated with icing/frosting/butter cream, sprinkles, fruits, or other toppings. 
CUPCAKE VS CUP CAKE
"Cup Cakes' was once different from Cupcakes. In the early 19th century when bakers developed their recipes based on cups (volume measurement), they introduced a new cake recipes: 1 cup of butter, 2 cups of sugar, 3 cups of flour, and 4 eggs. It is called 1234 cakes as well as Quarter Cakes. Because the new recipe was measured by cups instead of weight, it was also called "Cup Cake." Today, most people use both terms (cupcake and cup cake) to call a Cupcake. 
Photo by Evan-Amos
Cupcake tin with yellow cupcake paper liners. Spooning cake batter into liners. Note that it is filled only 3 quarters full for cake to rise after baking.
The first mention of Cupcake is from a 1796 cookbook called American Cookery by Amelia Simmons. In her book, Simmons suggests "A light Cake to bake in small cups."  The first Cupcake recipe was made in small tin cups, and recipe was found in Eliza Leslie's 1828 cookbook called "Seventy-five Receipts for Pastry, Cakes, and Sweetmeats." 
Before muffin tins were widely available, Cupcakes were often baked in individual pottery cups, ramekins, or molds. Around mid-19th century, paper lining molds and muffin tray was invented, and Nathaniel Waterman was the first to patent this "egg pan" (cast iron pan with multiple cup molds) in 1859.
In 1919, Hostess Cupcake was the first to produce and sell cupcake commercially, which each was sold for only five cents at that time. After WWII, paper liners specifically for cupcakes were available. During the 1950s, the paper baking cup gained popularity in the U.S. since it is convenient for making cupcakes as well as muffins. 
Cupcakes became a steady trend in the last 2 decades. There are cupcake cookbook that only introduces cupcake recipes. There are cupcake shops that only specialize in selling cupcakes.  Magnolia Bakery and Sprinkles Cupcakes are some of the earliest and most popular cupcake shops in United States. However, in 2014 there was an article about "the trendy cupcake bubble burst" when the cupcake chain, Crumbs Bake Shop, closed all of its remaining 48 stores. 
For cupcakes, you can choose any of your favorite cake recipe. Prepare muffin cups, cupcake liners, or any cupcake molds. Make the cake batter like you usually do. (Recipes can be found at the bottom of this page) Then, pour batter into cups until 3 quarters full only. (Give space for cake to rise) It usually takes around 18-20 minutes to set or use a toothpick to test. (Insert toothpick in center and see if it comes out clean)
Add frosting, icing, or butter cream with a spoon or piping bag. Decorate with your favorite toppings.
butter, sugar, flour, egg, frosting/icing
Toppings: Sprinkles, fruits, chocolate decoration
Pumpkin Spice Cupcake: http://www.chow.com
Chocolate Cupcake: http://sallysbakingaddiction.com
Red Velvet Cupcake: http://www.joyofbaking.com
The word, cake, is of Viking origin, from the Old Norse word "kaka".  The Oxford English Dictionary traces the English word cake back to the 13th century. In other languages, cake is translated to Gateau (Gateaux in plural) in French and Torte in German. 
Cakes can be savory or sweet, light or rich, porous or dense. Determining whether a given food should be classified as bread, cake, or pastry can be difficult.  For example, banana bread is a quick bread, but it has a texture of a cake and uses same ingredients as if a cake would have. There are many dispute on what category these desserts should be classified, but why don't we simply enjoy these goodies!
The earliest cakes were very different from what we have today. They were more like bread and usually made with simple ingredients like moistened crushed grains or nuts.  In Ancient Egypt, emmer and barley were used to make cakes, breads, and beer. Only the wealthy can enjoy cakes made with milled flour. There was no sugar at that time so honey was the primary sweetener. Sometimes, nuts and fruits like dates were added in the recipe too. 
In Asia, cakes were mainly made with rice, called rice cake. ("Nian Gao" in Chinese, "Mochi" in Japanese, "Tteok" in Korean)  It was first made around the period of Zhou Dynasty, 
Cakes covering with icing were first introduced in Europe around mid-17th century when cooking tools were more advanced and more ingredients were available. Icing was first made with only sugar and egg whites. 
Cakes were not only a meal or dessert to enjoy, it was used as symbols and representation for religious ceremonies and occasions celebrations from ancient times. Starting from at least the 8th century BC China, it was already a tradition to eat rice cakes during Chinese New Year for bringing good luck in the coming year. 
The first known birthday cake was recorded in the first century BCE from the book, Tristia, written by Latin poet Ovid. From his book, Ovid mentioned about celebrating his birthday with a birthday party and cake.  Today, cakes still play an important role in family gatherings, holiday celebrations, and ceremonial occasions like weddings, anniversaries, Christmas, etc.
In different cultures and regions, different cakes are made to celebrate the same holiday. For example, fruitcake is the Christmas cake consumed in France, Germany, and United States. In Japan, a frosted sponge cake with strawberries are more common during Christmas times.