A language family is a group of languages that all descend from a common ancestor, like a family of people or of HTML tags. The example I'll use here is the Indo-European language family. All the languages in this family are descended from Proto-Indo-European, an extinct language spoken in the northern Middle-East. It has several branches, all of which have smaller branches of their own, and smaller branches of their own, all the way down to dialects of a language.

The six main branches in this family are Germanic (English, Icelandic), Italic (Spanish, Latin), Indo-Iranian (Hindi, Perian), Hellenic (Greek), Celtic (Irish, Welsh), Balto-Slavik (Russian, Bulgarian). They are several smaller ones such as Anatolian that are lesser known.

The key to language families is macromigrations of people. This family is spoken by the Indo-Eurpean migration of people, who long ago spread into Europe, northern Asia, and Southern Asia. The migration split into smaller groups, the branches, as the Indo-Europeans spread out. The smaller migration that went to north Europe became the Germanic peoples, while the one that went to south Europe became the Italics. The one that went east into northern India and Iran became the Indo-Iranian, while the group that went into eastern Europe and north Asia became the Balto-Slaviks. These in turn diverged into even smaller groups, such as the West Germanic (English, German) and North Germanic (Norwegian, Icelandic).

A language family's size can be classified in the number of languages; number of speakers of the family's languages; and area, how widespread it is. Indo-European is not the largest in terms of languages (it only has around 450), but is the largest by area and number of speakers, with its languages being spoken all over six continents. The largest by number of languages would be the Niger-Congo Family in Sub-Saharan Africa. Families have a variety of sizes, from the tiny 2-language Koreanic family in Korea, to the large Sino-Tibetan in China and Tibet, to the Indo-European, and Afro-Asiatic of the Middle-east and northern Africa.

Now, on the smaller divisions of a family. I will use the classification of English as an example. We know that its family is Indo-European