As the amount of rowing/weights/cardio/etc sessions increase, the importance of having enough rest between sessions increases. Each time you train, you are causing changes in your body, such as muscle tissue breakdown and the depletion of energy stores (muscle glycogen), as well as fluid loss. By resting properly you are letting your body adapt to the training you are doing.
However, there is a fine balance to be maintained as too much rest will result in you not doing enough work to get your body to adapt at all, and too little rest will result in injury, sickness and/or being mentally burned out. It's not only your body that needs a rest, constantly pushing your self outside your limits in too many sessions each week will result in you not wanting to do it any more. Taking a mental break is just as important as a physical break. Again, this all comes back to
time management and setting aside time to wind down each week.
Too much training all at once will not make you fitter.
Some people are of the opinion that if they can train 3 time a day every day( just an example), then they'll get much fitter. But it is not during training that the body becomes stronger, its while at rest. The training you do must be gradually scaled up so your body has a chance to adjust.
If you miss out on proper rest.
Without proper rest, you will begin to experience performance decreases. You will feel more tired than usual and exercise will become more difficult because you are not recovering and are not prepared enough to handle the stress of another workout.
Active rest
If you feel like you want to do a bit extra training don't do some active recovery. Very, very, light cardio with plenty of
stretching will do much more for you than an extra full blown workout( unless you are doing very little in the first place, or, unless your body has adapted properly, in which case go right ahead).
Getting enough sleep
In general, one or two nights of poor or little sleep won't have much impact on performance, but consistently getting inadequate sleep can result in subtle changes in hormone levels, particularly those related to stress, muscle recovery and mood.
If you pay attention to how your body feels, and how motivated you are, it can be extremely helpful in determining your recovery needs( for example you might do with a few nights of better sleep, or more/better food after training session).