I was in the UK near Christmas and was planning on going to Stonehenge, but it was apparently closed. I figured that Stonehenge was a natural destination and anyone could basically just drive up to it. So what does it mean when it's "closed?"
Stonehenge is situated on the edge of Salisbury Plain and as such is clearly visible from the A303 and a minor road that passes it. Yes, you can just 'drive up to it'. Viewing it from the road is somewhat hazardous, however, there being no pedestrian footpaths along those roads.
The actual site is managed by English Heritage who control access, operate the visitor shop, cafe, museum and car park. If the Stonehenge is 'closed' it means that none of those facilities are available, and access to the space surrounding the stones won't be possible.
Note that the public are no longer allowed access to the stones themselves. The nearest one can get is about 10m away along a marked path. This is a sad reflection on the demands placed on such sites by visitors. (As a child in the Sixties I remember climbing on the stones!)
Stonehenge the tourist attraction is not just a natural destination. Like many sites that attract large numbers of visitors, there are timed tickets, admission fees, parking areas, a visitor center/exhibit, restroom, cafe, paved paths, shuttle buses, ropes to tell you where you can and can't stand, staff to oversee all this, etc... When the site is closed, that's all shut down. You can see this on a map of the site, which shows the pathways and areas for ticket holders.
However, it is possible to access the area without a ticket, and you can still see the stones from outside the ticketed area on a nearby road (though as noted in that article, parking on the road is not permitted) or if you hike in. This blog post provides further details and illustrates the view from outside the fence and its proximity to the paid area (which is also some distance away from the stones, except for special tours and the solstices).