Can someone please explain "database scaling" to a non-DBA?

I'm mostly a front-end developer but I know my way around relational databases well enough. I'm constantly seeing posts and articles about databases and applications having "scaling issues." At this point I just write it off as an arbitrary catch all buzz-phrase for a database can't do what the developer wants it to. Could someone get into specifics as to what this really means and maybe provide a few real world examples?