In fitness and workout terminology, the term "e1rm" is a short way of saying "estimated one-rep max". This is a term that is used most frequently when you are not testing your true 1-rep max, but are instead including other rep ranges in your workout. If you ever try to lift the most weight possible for an exercise, you will often see that absolute maximum referred to as your "1RM". When a lifter refers to their 1RM, that implies that the weight stated was actually lifted, while any reference to an E1RM implies that the weight is calculated.
The biggest benefit to calculating an E1RM after completing a set is to be able to compare that set to other sets of the same exercise that used different reps. Many workout routines do not have you test your 1RM frequently, as it is useful for both hypertrophy and strength to lift slightly less weight for more reps in a set. Comparing sets with either the same weight or the same reps is straightforward, but if both numbers change then it becomes more difficult.
As an example, say you completed a top set of bench press at 200lbs for 5 reps. During the next workout, you increase the weight to 210lbs, but are only able to complete 4 reps. Without calculating the E1RM for each of those sets, it's hard to know if you made improvement from one workout to the next.
There are a few different ways to calculate an E1RM. As you track workouts in TrackYourStrength, the E1RMs will be calculated for you for any exercise where you put in weight and reps. The formula used by TrackYourStrength is:
( Weight x Reps x 0.0333 ) + Weight
Taking the examples above, a set of bench press at 200lbs for 5 reps is an E1RM of 233.3, while a set at 210lbs for 4 reps is an E1RM of 237.9. This means that while you did less reps, it was a net improvement.
One thing I found out the hard way is that these estimated maxes aren't 100% accurate. I've taken my estimated max for a lift and tried to perform that for one rep, and it hasn't gone well. That said, there have been other times where I was able to do more than my E1RM stated. One main factor for this is that calculating your estimated max from a 2-rep set is very different from a 10-rep set. Less reps in the calculation is more likely to be accurate.
The other main factor is that it is a different skill to perform a lower weight for 10 reps in a row than to perform a maximum weight for a single rep. Failing your tenth rep means you still did 9 reps, while failing your 1RM attempt means you didn't get any reps. You also may be more used to the endurance needed for longer sets, or may be more used to holding heavy weight. These are both valid skills, and it helps to have both.
That said, you will still find it useful to have these E1RM numbers, but make sure to keep in mind that you can't assume that you could hit that max on any given day. By graphing your E1RM for each lift using TrackYourStrength, you can easily spot plateaus or progress across all of your workouts, regardless of the rep ranges you use on any given day.