Livery was often worn by the servants/household of a nobleman, often incorporating elements of the nobleman's coat of arms. Households would have "Livery Cupboards" for the storing of uniforms.
Livery could also be used by members of a particular group to show their connection. Chaucer's General Prologue to the Canterbury Tales mentions:
An Habersasshere and a Carpenter,
A Webbe, a Dyere, and a Tapycer —
And they were clothed alle in o lyveree
Of a solempne and greet fraternitee.
Ful fressh and newe hir geere apiked was;
[A Haberdasher and a Carpenter,
A Weaver, a Dyer, and a Tapestry-maker—
And they were clothed all in the same livery
Of a solemn and great guild.
Very fresh and new their gear was adorned;]
London's guilds and trade associations were called "livery companies" because of the specific forms of dress they would use to distinguish themselves. They also each developed a coat of arms (some of which are pictured above). They provided regulation and quality control over their particular field, and were the only legitimate source of training and commerce if you wished to apprentice. You were not allowed to ply your trade unless you were a member of the appropriate livery company.
In 1516 the existing 48 livery companies were given an order of preference by the Lord Mayor (mostly based on their wealth and influence), of which there were a dozen designated as the most important, the so-called "Great Twelve." Ultimately, there were (and still are) 110 livery companies in London. These days their chief purposes are charitable giving and networking, similar to Rotary.
Who were the 12 most important? I'll delay discussion on that until tomorrow.