Well, it is sort of hard to explain because we are talking about perceived soreness.
Also, I have observed that different people approach exercise in different ways. Some people are really nuts and exercise intensely until they nearly fall over. So these people would be well advised to moderate their intensity. Other people, never push themselves so they really don't see much in the way of improvement. The trick is to avoid the extremes.
I have found that if I get breathing hard and my quads start to ache and things sort of hurt then that is about hard enough. I can hold this for awhile. Of course, if I am riding any distance at all, doing this long is not smart. I have found that if I am a bit sore after the ride and a bit sore the next day, then that was intense enough. By "sore", I mean I am able to do things, I just feel a bit of an ache in my quads. Also the next day, I am able to do a recovery ride with no problem. I haven't found the need to ride more intensely then that just for conditioning.
I have even found that I don't even HAVE to ride that hard to get stronger. I have gone out west and ridden mountain passes. I would do a fair number of miles (over 50) and a fair amount of climbing (over 4,000') and do it day after day for a week or more. Now because I did not know what was around the next corner, I always do those rides at a moderate level of intensity - except for a few lapses. It doesn't make sense to hammer to the summet of a pass only to discover that the real summit is another couple of miles of climbing. The odd thing is that on getting home and riding my local hills, I discover that even this rather laid back approach has noticeably improved my climbing. I can usually climb everything in a gear or 2 higher. So quantity has a quality all its own.
So unless you are out to set records or something, just go out and ride. If you bear down a bit now and then and ride fast, that will probably help too.