Not sure what else to add to the definition, as it is covered from my perspective.
Perhaps if you want some more faux scientific information on aerobic and anaerobic facts....:
Aerobic running is about 20 x more efficient than anaerobic running. I read that somewhere, and what I think it means as that you can run a ton aerobically, where in comparison you can only run a limited about anaerobically.
There is nearly no limit to one's aerobic development. Obviously there is, but you can't do harm running aerobically for as long as you want.
Anaerobic running is approximately 20x more effective in provoking stimulus. So you may ask why not do a tonne of anaerobic running and get faster? Because again, you are limited, genetically-speaking. It only takes about 4 or 5 or 6 weeks to completely cap out the anaerobic limit for your training cycle. Then you are done. Time to race.
Lydiard felt that typical intervals like 1km or 1mile repetitions were not really "speed work" as people call it. Because you are not running THAT much faster than say you would in a 5K or 10K for example. Speed is really about nuero-muscular stimilus. So "speed" is very fast, like sprints and strides, where the longer intervals is just anaerobic work.
The purpose of anaerobic work isn't to simply "become faster, by going faster", but to bring down the condition so to repair/recover, so you are stronger again, but if you start doing anearobic work, be prepared to continue it for a few weeks.
Anaerobic work and racing should not happen during the aerobic period or "marathon phase" as he called it. That doesn't come until you are ready and all phases are completed properly.
Aerobic conditioning 8 to 12 weeks or for as long as possible
Hill phase 4 to 6 weeks
Anaerobic phase 4 to 6 weeks
Coordination phase 4 weeks
Taper 2 weeks
Each phase prepares you for the next phase.
Everything is important. Although I have talked to a lot of Lydiard-based coaches and very few do a proper hill phase the way Lydiard does it. Everything else within certain coach's trademark changes, to work for their athletes, takes place under the Lydiard principals of which there are five.
Two of my faves are: Feeling based training (like without GPS, Watch HRM) and Response Regulated training...you can follow a program, but every human is an experiment of one, so you may need to react and respond to run the best possible program.