My exercise and weight loss are almost independent of one another. I was active and exercised for a few years before I started counting calories in an effort to lose weight. The short version is I noticed I was more energetic, less prone to the blues/depression (especially in winter) and felt better overall when I made an effort to be more active.

I never, however, had a specific "fitness" goal in mind - I just moved my body, usually in the form of walking and climbing stairs (for 4 years I lived on the 7th floor of a building with no elevator, so there were LOTS of stairs). Strength training wasn't on the table until I started to lose weight and incorporated DVDs that used body weight exercises, as well as 3-5 lb. dumbbells.

Now, I'm thinking that some actual fitness goals would help ease the transition to maintenance and help me push myself a little. The problem is, I can't quite figure out what I should be aiming for.

What does it mean to be fit? All I can think of is the old Presidential Fitness Test we did in high school - and I was an obese teenager, so I'm pretty sure you can guess my feelings on that.

Should I be able to run a mile in a specific time, or do a certain number of sit-ups? Is it a combination of cardio/strength/flexibility?

How exactly does a person know whether or not they are "fit"?

If you can afford it hire a personal trainer to find you your fitness level and work from there... Or here is a Home Fitness Test you can try...

There really is no singular definition of "fit."
Being fit is a term thats kind of thrown around but the ACSM puts out guidelines for the definition of "active, moderately active, lightly active, and sedentary."
I believe that theres always room for improvement when it comes to fitness which in itself is a lifelong commitment. Being active will in turn improve fitness but I agree with Ilene. I would gauge your current fitness level and find your max heart rate and then work to improve your endurance and cardiovascular strength.
That should put you well on your way!