What is a unique visitor?
Squarespace defines a visitor as unique by tracking a browser cookie which expires after seven days. A visit is considered unique the first time the cookie is seen on your site. For example, the first time someone visits your site, the visit is considered unique. When this user returns, if their browser presents a cookie has previously been seen and has not yet expired, these visits are not counted as unique, regardless of their IP address. If this same user returns after seven days have passed, their return visit is considered unique. This also means that visitors who come to your site every day generally are not counted as unique until their browser cookie expires.
Are unique visitors the same as unique people?
No. There is no accurate method of tracking people visiting your web site. Instead, your unique visitor count can give you a rough approximation of how many people may be visiting your site. See this excellent post at the Omniture Blog (an enterprise analytics company) citing 15 reasons why your unique visitor counts calculated from web traffic won't be accurate.
If unique visitor counts are so inaccurate, what good are they?
Just because the number doesn't correlate exactly back to actual unique people doesn't imply that it's not useful. You can still use the count to track the relative success of your site over time. For instance, if in April you receive 1,000 unique visitors, and in May you receive 2,000 -- it would be safe to assume that website your traffic actually did double -- even if it might have doubled from ~800 (or ~1,200) actual, real people to twice that number.