Easy running should be done at an effort level of 65-79 percent of max heart rate. At this level of effort, you should feel comfortable, you should be able to utter a sentence without straining, but you should still have moderately elevated breathing. When you're training your body at this intensity, your heart, lungs, and legs will get significantly stronger over an extended period of time and coming into the season your aerobic system will be stronger, more developed, and ready to handle the more specific training that will drop your times.
When I started running I could barely run a mile in 7 minutes. After that, I just ran easy and did 2-3 strides a week for 3-5 months, albeit a measly 15-20 miles a week over that period. I time trialed a mile after and dropped down to 6:00. These are noobie gains, but I felt much more fit. And these easy runs were really easy; breathing was elevated but I was comfortable throughout the runs and ran my weekly mileage without getting hurt or strained. The day of the time trial I felt much more fit and way less winded after my first one or two laps which were 20 seconds faster than the splits I had on my first time trial.
TLDR:
This hobby jogger can confirm that easy runs do boost fitness substantially if done consistently and at an appropriate volume over a period of several months. Oh, and virtually all elite athletes at over 800 meters do the bulk of their mileage at an easy pace, so it should be a no brainer that it serves an important purpose to maintaining and stimulating fitness.