I get the opportunity to see lots of new riders on our group rides, and there's a common thread that shows up over and over.
Nearly everybody who is new is working out too hard, and many people are working out too much. What do I mean by this?
Well, to get better at cycling, you need to focus on both your anaerobic and aerobic systems. But the way you focus on these is totally different.
Your aerobic system training is best done at a fairly light intensity - one at which you can still talk comfortably. This is sometimes known as "base miles" or "LSD (Long Steady Distance)". This sort of riding helps your body get better at getting oxygen to your muscles, better at using your stored flat, and (very importantly) builds up your muscles and ligaments to deal with increased loads. Pros and races put in 1000s of miles at these sort of intensities.
I think of this sort of riding as setting your baseline.
Once the baseline is set - which is a 6-8 week process (or more) - then you can add some intensity to the mix to work on the anaerobic system. This involves interval work - things like 1 minute all out, 1 minute recovery, repeated 6 times, or hill repeats, where you do the same hillclimb over and over. The details are a subject of another post, but these workouts increase your ability to produce power, and your ability to deal with short exertions and recover quickly. And they're very small in quantity - you might only do 2 sets of 4 intervals in a workout.
This is also the time to add in tempo rides. Tempo rides are done right below around your lactate threshold (another big subject, but where your legs start to hurt when you're out of breath is a decent starting point) and last from 15 minutes to perhaps 30 minutes. Tempo rides improve your ability to deal with lactic acid, so that you can ride at a higher heart rate but still staying aerobic.
What I see in beginning riders is working out as hard as they can for the whole ride. And that works fairly well when you start riding - frankly, pretty much anything works well when you start riding - but it has problems once you start to get some fitness. That pace is fast enough that there is a significant anaerobic component, which is much faster than optimal to train your aerobic system. And, even though it feels like you're going really hard, you are riding too fast to be able to do your intervals all out.
So, if you want to get better, you need to get in the base miles, and then you need to have focused workouts of very high intensity with limited duration.