Overtraining is a very complex issue, and there is no simple answer.
And then we have to consider two types of overtraining: sympathetic (the sympathetic nervous system "speeds" things up like HR, respiration rate, metabolism...) and parasympathetic (the parasympathetic nervous system "slows" things down.) Obviously the signs and symptoms of these two types of overtraining are going to be opposite in some respects.
A simple definition, yes: overtraining is an imbalance between training and recovery.
Markers for overtraining: There is no single marker of overtraining that we can look at and say... "NOW, he/she is overtrained."
- testosterone/cortisol ratio: requires blood test, and is not a totally consistent marker, although it is worth checking in some athletes.
- increased resting HR (sympathetic OT): certainly easy enough to check your resting HR before you get out of bed in the morning. If it elevates and stays elevated, that is certainly reason for concern.
- decreased resting HR (parasympathetic OT): very difficult to tell if the decreased HR is a positive training effect or a possible result of overtraining.
- unusual fatigue: of course we are all tired from training, but if you are still fatigued 48 hours after a strenuous workout, that is reason to be concerned.
- lack of enjoyment of training or sport... depression: Obviously there are several reasons for depression and lack of enjoyment of the activity. Overtraining is certainly a possibility.
- muscle injuries, unusual soreness, soreness that does not go away: may be the best "sign" for bodybuilders/recreational weight trainers.
Suggestions: Monitor the estimated volume load of training (sets X reps X load). Limit increases in volume load to no more than 10% per week. Read a bit about overtraining, and the other possible signs and symptoms. If you think you are moving in that direction, back off.
True overtraining syndrome can cause problems with the musculoskeletal, nervous, endocrine, immune, and cardiovascular systems. True overtraining can affect performance/training for up to a year. Be smart, train smart, read, be aware of your body and what your body is telling you.
This is a brief overview. It is more complicated than this, but this is a start.