As a recruiter, I've seen lack of flexibility on the recruiting side with employers clinging to every last detail in their ideal spec while perfectly good candidates get overlooked. As a career coach, I see jobseekers prematurely dismissing possible targets waiting for that perfect job. It's true that you want to be focused in your job search (otherwise you dilute your efforts and come across as scattered and possibly desperate). But it's equally important to be flexible so you don't miss opportunities, you react to market feedback and changes, and you refine your approach for your intended audience. How do you know if you are flexible or just unfocused?
A flexible job search recognizes that there will be multiple possible targets. Each of these targets however is focused on an industry, function and geography. So you might be looking at an HR generalist spot within financial services - banking in NY. The focus is on generalist (as opposed to recruiting or compensation or some other area of HR) and on banking (as opposed to accounting or insurance or non-financial services areas) and in NY. This candidate might decide to also look at compensation and/or other areas within financial services or expand the geography, but s/he is focused within each target.
A flexible candidate tailors responses to job descriptions to highlight what s/he has and to outline specific plans to cover what's missing. This jobseeker is focused on responding to the market need. S/he doesn't dismiss an opportunity outright it there isn't a 100% match, but s/he does address the deficit. An unfocused candidate responds generally to lots of job descriptions but doesn't tailor the message. That's not flexibility; that's a scattershot approach.
A flexible candidate goes after the best job, not the perfect job. People can expect to change jobs and even careers multiple times in their lifetime. Sometimes a job is good for a current situation (e.g., a more flexible job when there are family issues to balance, an international post because your target role demands that experience). But situations change. Preferences change. What is available in the market changes. A flexible candidate recognizes that the best job is a match between what s/he wants and what the market will bear. Many jobseekers are coming off of a long-time unemployment, and financial obligations loom large. You might have to take a stopgap job now and table a longer-term search for when you are back on your feet financially. That's being flexible. If you never do get back to that long-term career goal, however, that's unfocused.
Flexibility respects market conditions, timing, personal life circumstances, and other variables in the job search. Be flexible, but stay focused on your long-term goal even as you take the whole picture into account.