Short answer? It depends.
The more often you train, the more results you will see.... to an extent. How much you train isn't as important as how well you recover.
How well you recover is highly individual, and a product of multiple factors...
First, take a 22 years old with an athletic background? She's fresh out of college, where she ran track, is working reasonable hours and has a sunny-disposition. She can probably train 2x a day for 7 days a week, eat pizza, and make still progress.
How about the 45 years old guy who's overworked? He's been working at a dead-end job for 15 years, has slowly gained weight and takes melatonin to get to sleep every night. His recovery abilities probably aren't quite as generous as they used to be. He will need to be more conscious of how he sleeps, what he eats, and how he spends his downtime.
The one thing both of these people have in common? Good habits will maximize their results.
2. Training Experience (aka Training Age)
If you have experience with resistance or cardiovascular training you can usually train more often than a brand-spankin'-new beginner.
Being able to train twice a day is one thing, but you also need time to recover from every session you put your body through. That includes extra sleep (quality sleep), and time to prepare proper meals to meet the needs of your recovering body (which is literally re-building the tissues you damaged during your training session).
4. Type of Training
Some types of training take more of a toll on your body than others. For example, long-distance running and heavy resistance training can be devastating to your body, and leave you walking with less than a spring in your step for days following.
Lighter resistance days or short/high-intensity workouts will usually allow you to bounce back much quicker. This allows you to accumulate more training volume over multiple sessions than you could have in the single, much more demanding, session.
Keep in mind, the grueling long-distance runs and the heavy-double resistance days have their place, but you don't need to be training that way every week.
5. What are your goals?
If you have more demanding goals, you will need to have higher training demands. This means not only training hard but also training smart.
However, if your goals are general health, or if you just want a Physical Abilities Test (PAT) time that meets your application requirement, you can trade in the 'extra' training days and replace it with the activities that make life worth living. Not feeling the gym today? Take a hike (in the literal sense), go for a bike ride, or even just a walk around the block.
*6. A great recovery day is better than a poor training day
I don't mean you get to sit on your butt and binge-watch Scandal. But taking a day out of the gym and spending it with your family or friends can be just as valuable as yet another day in the gym, as long as you've earned it. Sprinkle in a short recovery style workout (ex: 1 min skipping, 25 BW Squats, 15 Push Ups, 30 walking lunges, FINISH), and 10 minutes of mobility work and your day off can have just as positive of an effect on your training.
But Mark.... How often should I train!?!
Ok, fine. I'll give you some actionable guidelines. However, understand that the below recommendations are extremely general, and how often you train combined with what type of training you are doing is something you need to figure out on your own (or, preferably, with the guidance of a great trainer.
Here are some basics:
Strength and Resistance: As a general guideline, if you're new to strength/resistance training I would recommend training 2-3 times per week. Use your soreness as a judgment on how much you can handle.
Cardiovascular/Aerobic Conditioning: If you are performing High-Intensity Interval Training (HIIT), I would recommend training 3 times per week.
B.Kin, Canadian Society of Exercise Physiology CPT