Wild Cave Tours are guided tours into caves, either in undeveloped parts of a show cave or in a nearby "wild" cave. The tour is very similar to a real caving tour, there is no light and no paths. But there is a guide, normally most of the equipment is provided, and it costs a fee.
Most caving clubs make very similar tours for new members. Normally there is no fee, despite the members fee. So it is much better to look for a caving club nearby, become member, and do some caving. But this trips offer people a chance to get a taste of what caving is like, before they join a caving club.
Most of those tours are connected to a show caves. Some of them are made by adventure companies, where caving is another extreme sport beneath bungy jumping and canyoning. I heard many bad critics about those tours, especially because of the sometimes very poor knowledge of the guides. So have a good look at the company and the guy!