Just as being in a relationship can make you more attractive to others, having a job can make you more attractive to employers.
Why? It’s a brutal feature of human psychology: People want what they can’t have, and if someone else has you (either as a mate or as an employee), an observer will want you more. If you’re a free agent, a potential mate or potential employer may see you out there alone and think, “Sure, this person looks good, but why isn’t he/she married/employed already? What’s wrong with him/her that I’m not seeing? And why would I want to take a chance?”
If you’re sending your résumé out, it’s usually to your advantage if you already have a job while you’re looking for a new one. Other than the obvious perks of enjoying a steady income and avoiding a stressful employment gap, being employed shows a potential new employer that you’re not desperate for work; if you apply for an opening, it’s because you want it, not because you need it. It puts you in control and prevents you from appearing desperate.
I always advise clients, who are often so confident in their new résumés and excited to start sending it out, not to quit their jobs prematurely for these very reasons.
Of course, there may be compelling reasons to leave without a new job lined up — an intolerably toxic work environment, an impossible schedule that won’t allow you to interview for new jobs, or pressing family obligations that you hope a new position will be more accommodating for. Everybody’s situation is different.
But if it’s at all possible, don’t let go of the old job until you’ve landed a new one.