Unfortunately, there’s no straightforward answer to this one.
Sweating helps your body regulate its core temperature, and your sweat rate is influenced by a number of factors, including genetics, gender, and the weather.
Several studies have shown that better athletes do, indeed, sweat more. One such study, published in the journal Experimental Physiology in 2010, demonstrated that both male and female athletes sweat more than their untrained counterparts, leading to the conclusion that training improves the sweating response. More sweat, they thought, allows athletes to dissipate heat more quickly so they can stay cool during strenuous workouts.
However, if you’ve noticed an increase in your own sweat rate, don’t go bragging to your buddies about it just yet.
A 2011 study published in the American Journal of Physiology found that sweat rate depends on your physical work and your body’s surface area rather than on VO2 max. In other words, you’ll sweat the same amount running a seven-minute mile whether you’re in tip top shape or not, assuming you haven’t gained or lost any weight. This study concludes that sweat is an indicator of the physical work you’re doing, not how fit you are. (Read more about this study at Sweat Science.)
Want an indication—unrelated to your sweat—that your fitness is improving? Try doing a benchmark test where you repeat the same workout once a month so you can document any changes.