Ask any American to list the rights enshrined by the United States Constitution and they'll be awfully quick to tell you the first two. Hell, take a drive on any freeway in America and you'll see a couple of bumper stickers supporting the right to free speech and right to bear arms.
Then, there's the third amendment, which states, "no soldier shall, in time of peace be quartered in any house, without the consent of the owner, nor in time of war, but in a manner to be prescribed by law."
It remains the least controversial amendment in the Constitution and is rarely litigated. To date, there has never been a Supreme Court ruling that has used the third for the basis of a decision. Today, the idea of troops seizing and occupying a U.S. citizen's home sounds absurd. Unfortunately, this wasn't the case back when the Constitution was written.
In 1765, the British Parliament needed to shelter their troops as they fought in the French and Indian War. So, the Crown did what they liked to do and made a decision that benefited British troops. They enacted the Quartering Acts of 1765, which stated that inns, stables, taverns, and wineries were required to house troops at the discretion of a British officer. Troops were allowed to take as they pleased, which would run taverns and wineries dry.
The cost of quartering troops would often fall on the shoulders of local business owners. Eventually, their expenses were reimbursed by colonial authorities — not the British government. Soon, British troops started taking refuge in private homes. Without fear of penalty, they could barge into your house, kick you out of your bed, take your food, and tell you that you'd (maybe) be paid back in a few months.
To the colonists, this was a headache, but at least there was a reason for it — for a time. After the French and Indian War ended, the British troops continued to use private residences. Many returned to their own fortifications, but many others continued to exploit the Quartering Acts for their own gain.
This, coupled with the fact that the colonists were still paying for a foreign standing Army for no discernible reason, fostered resentment towards the British by many Americans. Then, the Boston Tea Party happened. The Brits saw a rebellion brewing and enacted the Quartering Acts of 1774. This time around, it clearly gave all British troops the right to occupy any building they saw fit without any obligation to reimburse the owner.
Most colonists weren't personally affected by the tea tax and were simply inconvenienced by the stamp tax. Having Brits come into your home without warning or cause and being forced to give them whatever they pleased, however, was the straw that broke many colonists' back.
When the dust settled and the American colonists became American citizens, one of the concerns they voiced most was that something like the Quartering Acts never happen again. And it became so when it was enshrined in the Bill of Rights and became the Third Amendment of the U.S. Constitution.