The 1RM (One Rep Max or One Repetition Maximum) is the weight you can do exactly 1 rep with. For example, if you did a set of 100 kg for 7 reps, you can use a 1RM calculator to work out that your 1RM was 120 kg. That means you could have done 120 kg for 1 rep.
Since your 1RM strength is normalized to 1 rep, sets with different reps are comparable. For example, if you do a set with 105 kg for 8 reps and another with 95 kg for 12 reps, the 1RM is 129 kg in both cases. This way, you can immediately see that your performance was the same in both sets.
Also, the 10RM can be used to evaluate your progress very well: If the 1RM increases (in the long term), you will become 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 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 that 10 reps are probably much closer to what you're aiming for in most sets. This makes it 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 in the graphs. You can immediately see from the graph if you are progressing.
An often-used alternative to the 1RM is training volume. However, this is inferior because it "rewards" high reps far too much. By only considering the training volume, you could have a "fake progression" by doing more reps and using far less weight.