The way it was explained to me a long time ago, (before we had HRMs), is when you mash the pedals, you won't get the blood circulation that you need to supply your muscles with nutrients and take away the wastes. So eventually you will fatigue. If you spin the pedals a little faster, you will use more energy but your muscles will get fed and wastes will be taken away.
Say what? Is this similar to the "if you work too hard too soon, you will burst the capillaries that you have built up from aerobic/base work"? How long ago was this explained to you...as current exercise physiology (and any coach that reads and thinks) would disagree with this theory.
Now today we have Heart Rate monitors and can guage how much work we are doing. It's not the only tool, but its a good one. Others are Power Taps, perceived effort and your speed. I sure someone will suggest more.
The only thing a HRM tells you is how fast your heart is beating...it does NOT tell you (not without a relatively large margin of error) how much work you're doing. The power-measurement tools (SRM, Powertap, Ergemo, Polar) do tell you how much work is accomplished, usually in terms of kJ.
Spinning is more efficient on flat roads because in addition to pushing down on the pedals, you will be pulling back, pulling up and pushing forward. This uses more different muscles in your legs. Mashing will use fewer muscles more of the time, and on only part of the pedal stroke. You will have to spin with some degree of effort to gain fitness but it will be much more efficient energy transfer from legs to cranks.
For two given cadences, the lower one will be more "efficient" in terms of oxygen consumption and work accomplished...this has been shown time and time again. It's not necessarily "better" to be the most efficient though, as most endurance sports I know measure time over a distance, and not how long/far you can travel than somebody else. "Mashing" (lower cadence) versus "Spinning" (higher cadence) will solicit tend to solicit MORE muscle fibers per pedal stroke, given the same power output.
All of the books that Julian suggested are great sources, I have thumbed through the first two and own the last one "The Triathletes Training Bible". I also recommend "Triathlon 101", "Swim, Bike, Run" and "Triathlete Magazine's Complete Triathlon Book"

My $.02

jaretj

Don't want to seem like an ass (which I readily admit I am sometimes), but I just had to point that out.
In my experience, most endurance athletes are relative naive when it comes to the actual physical adaptations of the human body to training. There are no magic pills...you figure out how often/much you can train (hours or miles/km), and you train only as hard as you can to elicit adaptation from week to week (or month to month, even year to year). The trick is to figure out how much stress YOUR body can take and still adapt and not "over-train"...and for that science does not have a firm answer. That's partially where the "art" of coaching comes in, and an area which some self-coached athletes just naturally grasp.

Yes, I totally agree that for many athletes there's a time to build "base"...to get the sea legs back, if you will. If they took some time off, maybe it's to lose weight/increase lean muscle mass, increase blood plasma levels, increase hematocrit, increase muscle capillarization, increase mitochondrial content...or any of a number of other adaptations to training that has been documented. How long does this take? How long do you have? You have to train fast (higher power output) to go fast...there's no getting around it. You want to average 250 watts in a 40km TT, then you have to be able to do that in training, broken up into intervals. Same with 6:30min/mi...or any other example you can think of. Specificity is a major factor in training...

OK...off the soapbox. Back to work...thanks for reading, if you got far without falling asleep.

Take care...and for those of y'all in SoCal...hope you and your family are doing ok.

Dave

PS: One of my favorite quotes ever, and IIRC it's from Greg LeMond (the OTHER American TdF winner), and it's something like "It never gets easier, you just go faster."