The 1RM (One Rep Max or One Repetition Maximum) is the weight that you can lift for exactly 1 rep on a given exercise. For example, if you did a set of 200 lbs for 7 reps, you can use a 1RM calculator to work out that your 1RM is 240 lbs. That means that you could have done 240 lbs for 1 rep.
Since your 1RM strength is normalized to 1 rep, you can compare this with sets that use a different number of reps. For example, if you do a set with 215 lbs for 8 reps and another with 185 for 12 reps, the 1RM is 200 lbs in both cases. This way, you can immediately see that your performance was the same in both sets.
Also, the 1RM can be used to evaluate your progress very well: If the 1RM increases (in the long term), you are becoming stronger—no matter what the weight and reps look like.
To find out what your 1RM is for a particular exercise, check out our Rep Max calculator.
In addition to the 1RM, there is also the 10RM, which follows the same principle but - as the name implies - calculates how much weight you can move for 10 reps. This has the advantage of being closer to what you're likely aiming for in most of your sets, since you will do 10-rep sets a lot more often than 1-rep ones. This makes the 10RM easier to interpret. This is why we use the 10RM in the Alpha Progression app. It is automatically calculated for each set.
You can also see the development of the 1RM of an exercise over time in the graphs displayed by the app. You can immediately see from the graph if you are progressing.
An often-used alternative to the 1RM is training volume. However, this is an inferior type of measurement because it "rewards" sets with high reps and lower weights far too much. By only considering the training volume, you could see a "fake progression" if you do more reps and use far less weight.