Vietnhi Phuvan makes a good point in the comments - there is no single answer, or even group of answers, that will answer this question. OP should make this more specific (maybe "senior applying for junior roles in same industry?), this question is otherwise mega broad.
For example, I'm a CFA approved stockbroker, and I apply for a bartender in a club. Now, I'm obviously overqualified for this role, but I can probably argue that I'm a bit burnt out, want to work in a bar, passionate about partying, I don't know, something along those lines. That sounds like a fair argument.
Now, take me as the CFA approved broker, and watch me apply for a role as a, I don't know, children's bus driver? Again overqualified, but this time if I use that "passionate about partying" line they're probably going to call the police and lock me away.
So the first question you should be asking is why am i applying for a role that i am overqualified for?. You don't mention that, and if you had a valid reason I imagine you wouldn't be asking this question... so to make this answer even vaguely useful, I'm going to assume you need the money. Also, that you're a senior {something} applying for junior {something} roles.
The problem with explaining this is that finding people is hard, and everyone suspects that the first job they give someone who is currently unemployed is just going to be used by that person as a springboard to a better job. Hiring you from Alpha company to Beta company - well, you're giving up Alpha, there must be something about Beta that you like, that goes above and beyond just giving you a paycheque. Hiring from unemployed to Beta, and they'll suspect you want the money. And that means that you'll then jump from Beta to Alpha because you're actually more keen on Alpha's domain, tech, whatever. And now the folks at Beta have to hire again. Yuck, pass.
Sadly, this same argument is doubly true when you're overqualified - they'll just assume you're going to cut and run.
None of this is helpful to you, but I do have one semi-generic response that might come in handy. Apply for roles that are outside your domain - banking domain? Apply to ecommerce companies. Ecommerce domain? Apply to Marketing comapnies. That way, you can explain that you'd like exposure to the domain, and you feel that while you have a lot of value-add from experience in {old domain} you'd like to get more exposure to {new domain} to feel comfortable working there.
Again, this is only in the case where you're a senior {some role} applying for a junior {some role}, not where you're that burnt out broker trying to drive children to and from school. That ship has sailed man.
Oh! Or just fudge your CV a bit and make yourself sound more junior. You didn't lead that project - you were lead in that project, for example.