The main signal to your body that it needs to do more building is to use it.
That's where the exercise comes in. While you're exercising, as my sketch suggests, you're taxing your fitness. At the end of a workout, you're in slightly worse shape than if you had done nothing. But! Your body looks at those fatigued muscles, and the micro-tears, the depleted enzyme stores, and so on and realizes that you need stronger muscles and more enzymes and such. The tears are the signal to rebuild the muscles stronger. If they were strong enough already, they wouldn't have (micro!)-torn. And so on throughout the body and its systems that you taxed by exercise.
That is the recover phase. How fast you recover and how much above your original fitness level you go varies by person. And as you age, the recovery takes longer and you don't go as high above the previous baseline. But you do recover, and you do move above where you'd be if you didn't exercise at all. When you're younger, the recovery from a hard workout is something like 24 hours. When you're older, it's more like 36 hours. And still later, it's more like 48. One problem being, 'younger', 'older', and 'still older' all depend on the person. So does 'hard workout'. Hard workout itself will change as you get more fit, as well.
Training is that combination of stress AND recovery. You challenge your body in some way, whether by lifting a weight, going for a longer walk than usual, running instead of walking, ..., and then it rebuilds itself to be able to manage that challenge more easily. The 'stress' is defining 'hard workout'. If you can do a workout day after day and never experience a decline in performance, it isn't a hard workout any more. It isn't providing a challenge for your body to deal with.
I can now, for instance, walk a mile a day, every day, and would get essentially no training from it. My current condition is good enough that all the muscles, ligaments, tendons, enzymes, lung capacity, and on, would not consider the 1 mile walk to be a challenge. On the other hand, they do currently consider 32 minutes of run/walk to be a challenge. So that is my hard workout. After a while, as I continue to do my workouts, it'll be 32 minutes of running straight through that I need to do in order to challenge my body. And later still, it'll be 60 minutes on trails (fun!). At that time, 30 minutes running will be an easy day, that needs little recovery time.
What is a hard workout for you, today, is probably different than what it is for me. What is hard for you today, after 3 months of regular exercise, you'll be calling easy. As long as you provide the training challenge AND time for recovery.
Stresses and recovery are also fairly specific. It means that if I did a hard running workout today (my 32 minutes of running 3 minutes and walking 1, currently), that I should not do that workout again tomorrow. (I need 36 hours recovery time from a hard workout.) But I can certainly, and plan to, go to the gym and do a weights workout, particularly one that is not stressing the muscles I use most heavily in running. Folks who mostly do weights tend to arrive at a rotation -- lower body today, upper body tomorrow, core muscles the day after, a day of full rest and then repeat the cycle. And, of course, many variations on that theme, giving themselves the 36-72 hours recovery/rebuilding time they need. (It seems that strength work takes longer to recover from than running does.) I could also alternate my running workouts with swimming. Different muscle groups are emphasized.
The ACSM recommendation of 5 days a week of moderate aerobic exercise, or 3 days a week of vigorous, as a baseline is perfectly consistent with what I'm suggesting here. What I'm calling hard, is pretty much what they're calling vigorous. You can only do those about 3 days a week. The moderate workouts need less recovery, if any, so you can do them 5 days a week. Remember, too, that they're talking about a baseline, a low end. It would be good (there are health benefits) to go beyond that level. Such as my target of 5 days a week aerobic, with 2-3 days of it being vigorous.
There's a different issue of difference between my diagram and what the ACSM suggests. (Which one of us is the expert?) In labelling the vertical 'fitness', I was taking a very narrow definition. Namely, how well you can do your exercise. You can maintain current ability with only 2-3 runs per week and 1-2 strength workouts. They have to be hard runs or workouts, but it can be done. The recommendation exceeds that because whole life health benefits show improvement with doing more exercise. Keeping your bad cholesterol down and good cholesterol up benefits from the extra days. You also get to be a better runner, and stronger, if you're doing the extra days of exercise.
You'll notice, I hope, that neither the ACSM nor I said a word about how fast you should run in any absolute sense (your vigorous might be impossibly fast for me, but you and I can both go out and do a workout hard enough that we don't feel like talking during it). The health benefits don't seem to care about that. They do care about you doing something that gets your pulse up for 30 minutes (total, ACSM also mentions that 3 sessions of 10 minutes in a day seem to be equivalent to 1 session of 30) a few times per week.
Different reminder, as people do have a tendency to think if a little is good, more must be better. The stress you impose has to be one that you can recover from before the next workout. And you should be doing those 3-5 workouts per week. This won't happen if you run so far or fast or both that you can't run for a week. Or, worse, that you get injured and need to take several weeks off. That's several weeks of continuing decline, plus the damage you need to recover from when you can finally get back to work.
Of course, one of the ways I know about mistakes you can make in your training is that I have made them. Hence my current (first, and hopefully only) rehabilitation. Still, I've usually caught myself before the point of actual injury.