I call it FU savings. Mainly because if you get tired of your employer, you can tell them to take their job and shove it. Move on to better pastures, and not have to worry about paying bills while you look.
I've done it twice, and there's nothing like having that fund (and also being unsecured debt-free) backing you up. Each time I made my choice to leave my employer, I had a new job lined up within a couple of months - and I had negotiated a higher salary to boot.
The best way to go about getting such a savings set up is to first plan a realistic budget. Then, pay down any unsecured debt, starting with the smallest debt owed first. Roll that payment, once the debt is paid back, into the next debt, until you have all your debt paid off.
At that point, you should be left with no unsecured debt; a mortgage can be considered OK (as it is secured by your equity) - but if you can pay that off too, so much the better. Usually, though, it's better to keep it for tax deduction purposes.
Don't have a car payment - if you aren't paying cash for a used (but reliable) car, and paying for it in full - you are likely wasting your money.
There's more tips out there than just the above, but them's the basics - basically. Once you become "debt free" in this manner - a great burden will be lifted from your shoulders. I'm serious.
And once you get your FU savings set up (bank for at least 6 months to a year - but ultimately, just keep building the savings as you have available cash - you may never know when you'll need it) - you'll be free to do as you please with your career and goals.