I just carry a small notebook with me to the gym. I note the reps and weight, and any subjective notes about what worked, what didn't, and what to aim for next time.

Takes a few seconds to fill out in between reps.

I'm sure there are useful, simple apps, but you don't need an app to track.

As others mentioned, tracking lets you make sure you're increasing your lifts. I never progressed consistently until I started tracking, and slightly increasing each time.