Your leverage is something like, 'Everything someone wants that they think you can give them, or take from them, for which they think they have no acceptable, (in terms of their culture,) alternatives that aren't more costly than whatever you'd impose on them in return.'
There's also an aspect of norms to it - most commonly in terms of consistency because people generally want to appear reasonable.
Anyway, if you've already got a job, their position looks worse in that respect since you need them less. Though that doesn't necessarily give you any more leverage in terms of extracting concessions from them since your job doesn't necessarily make you a more desirable employee.
Though, for some reason, companies seem to hang themselves in that regard - placing a great emphasis on whether you're unemployed, (which, personally, I've never found to be a great predictor.) So, while it's not an 'of necessity' thing, it probably does convert into some leverage on your part for a lot of potential jobs.
It is, in a round about way, why it's generally better to try to bargain about wages after you've got some sort of buy-in established on their side. Since you'll have the greatest leverage once they've decided they want you.
Things that you can point to that you can quantify, that's generally a good source of leverage - especially if you're a contractor. Anything I do that I can hang any sort of number on, I write down to use in interviews - not all of it goes onto my CV.