The Purpose of Recording Strength Training?

People like to keep track of their ability to lift heavier things and more times (reps).

I have the same question

You record strength training workouts to see how you're going compared to your training program, and to be able to look back and view your progress. I wouldn't recommend recording this in MFP though. My preference is a regular notebook.

For the same reasons you track anything you do to be fit.
Losing weight or counting calories is not part of everyone's goals.
http://www.myfitnesspal.com/blog/Robin_Bin/view/reasons-why-we-re-all-here-297995

One of the first principles of strength training is progressive overload. In order to make gains in strength, you must perform more work. This can be quantified by doing more sets, more reps, or more weight in the same amount of time. Or, by doing at least the same amount of work in less time. The purpose of tracking your strength training is, thus, to keep a record of what you've done, so that you can accurately gauge whether you are making progress. If you are doing a number of exercises each day with different weights that are varying, it's very difficult to keep track of all this only in your head. You also won't have information to refer to if -- a year or two from now after falling back out of shape -- you want to replicate the exercise of a particularly successful time in your life.

The same principle also applies to cardiovascular training. If you always run (or bicycle, swim, etc.) at the same speed for the same time, you will not improve your cardiovascular system. Of course, if you are only using exercise to burn calories, rather than improve your fitness, you can get away with not working out in a progressive manner (although adaptation will cause repeating the same exercise at the same intensity to become somewhat less effective over time).

Strength training in a progressive manner will help ensure that you preserve your existing muscle mass while trying to lose bodyweight. This is very important. If you don't preserve this mass, you can end up weighing somewhat less on the scale without significantly altering the amount of bodyfat you have. In this case, you may actually look worse than when you started. This point shouldn't be exaggerated -- your body wants to keep its muscle mass -- but it can happen with crash dieting and certain other diet and exercise extremes.

If your goal is to improve your muscle tone or gain muscle mass, it's also important to strength train in a progressive manner. Muscle tone is primarily determined by the residual contraction of your muscles in a resting state, which progressive strength training increases, and your overall level of bodyfat. Firming up arm flab, for example, is about losing weight and increasing performance on arm exercises. For this purpose, it's much more effective to use a challenging weight for a smaller number of reps than it is to do use light weights for very large numbers, especially if you have never increased the weight. Misconceptions abound, especially among new and female exercisers, with regards to "toning" and "firming" up problematic areas of the body.

If you're trying to gain muscle mass, you have to couple strength training with a diet and overall training volume that supports growth. Muscle is metabolically active tissue -- having more of it will raise your basal metabolic rate, which means your body will burn more calories at rest.

A bit of additional (but related) information, but I hope that helps.

strength training is incredibly important not just in regards to getting stronger but in losing weight as well. this site is ridiculous for not including the calories burned from it but here's why you should include it: as we all know and despise weight fluctuates. Lets say you've stayed under calorie yet you gained weight..by looking back on your strength training you can see its obviously because you gained muscle since we all know muscle weighs more. It is more for you to keep accurate record and focus on what works to gain muscle and lose weight as well as see what works in general...plus seeing it keeps you motivated