This video explains what a rights-managed stock image is. Here is also a written explanation.
When you purchase a rights-managed license to an image, video or other media product, you purhase a right to use the product in a specific way. Often, this will define the image size and resolution of the product, the geographical area where the product will be used, medium in which the product will be used, for how long it will be used, number of copies in case of printed media, etc.
For instance, you may purchase a rights-managed license to an image which allows you to use it in a marketing brochure with a limit of 2,500 printed copies in a specific language and country. Or you could purchase a license that stipulates that you could use the image on your website with a worldwide reach, for 5 years.
Similarly to a royalty-free license, a rights-managed license can often also be purchased by several users, and therefore several users can use the same product. If this is the case for a particular license, it means that you share the right to use the media product with other purchasers.
However, a rights-managed license can also be an exclusive. If this is how the license is drawn up, you would have exclusive right to use the media product. If this is not clearly stated on the image profile, it is fair to assume that the image is only exclusive if the price for the license is very high.
Also, as with a royalty-free license, you do not own the copyright to the product, nor do you own the product itself. You simply own the right to use it for the agreed purpose and duration.