With Galleries, you essentially become a curator of all the creative work around Flickr. Each Gallery can contain up to 18 public images or videos from other Flickr members.
We imagine one of the first questions is, "Why only 18?" Flickr explains in the FAQ that the limitation is meant to encourage a workflow more like what a curator of a museum or gallery might do when selecting works for an exhibit. Think of it as perhaps similar to Flickr's 90 second rule for video; we wrote recently about why such creative limitations can be a good thing.
To create a new gallery, just select the "Add to Gallery" option at the upper right of public photos or videos. If you don't see the icon, it's most likely because that Flickr member has disallowed the use of their images in galleries.