Hmm, well I’m sure in theory there are several ways you could do something like that. You could just have images on a page that link to other pages where you’ve created standard galleries.
Or you could have a post grid somewhere and on each single post, you could have a standard gallery of images.
What I mean when I say a standard WordPress gallery: https://vimeo.com/16686184
You could also look into using a plugin like NextGEN: http://wordpress.org/extend/plugins/nextgen-gallery/