No, a domain can't read cookies set by another domain.
Here's how it works: a publisher (eg. 'travel.com') will place a snippet of JS or an image from a tracker (eg. 'tracker.com') on its site - anything to initiate a HTTP request. The HTTP response from 'tracker.com' will set a 'tracker.com' cookie in your browser. This cookie will contain a unique identifier, which links to a backend database at 'tracker.com', which will now contain the fact that you visited 'travel.com'. Sometimes 'travel.com' will use JS to add parameters to the HTTP request to 'tracker.com', to pass things like gender or age or location, should they know that about you. This information is also added to the database at 'tracker.com', keyed to the unique identifier in your cookie.
You'll then go to another site, which will make a request for an advertisement. The request might be directly to 'tracker.com', or it might be to another domain which will return JS which will then force an HTTP request to 'tracker.com'... there could be many redirects, but an HTTP request to 'tracker.com' is involved, which automatically contains the unique identifier in your cookie.
'Tracker.com' then uses that unique ID to look up what it knows about you, potentially supplements that with location based off your IP address, and potentially appends some guesses about demographic info made from the content of the site you're visiting and the type of folks that tend to live in your ZIP code. It then uses all of this (or passes all of this on to another party) to select a related advertisement. That's why you see ads for cars after visiting car sites, and ads for travel after visiting travel sites.
There's nuances, of course, but that's the gist of it.
Wow, I visited the Capital One page for myself and was pretty amazed with the results: interests where right aligned.
I got different pages when switching browser (although you have to clear cookies/flash cookies), and also different credit card proposals (some student cards for you in Chrome? Or rather some "serious" cards in Internet Explorer)
You can find the tracking from the domain .edge.ru4.com. It does contain a wealth of information, although I have yet to find the identifier for "my" Nielsen Market Segment. The segments are here:
