One means one set of pushups, no rests.

Maxreps means do pushups until you can't do another, despite digging really deep.

It was just shorthand to say "in the ballpark of what the maximum you can do in one set is" (note the tilde).

I'm not suggesting you destroy yourself every day. Just that you continuously increase the number as your endurance improves over time. It levels off at some point, in my experience this never becomes a session taking more than three minutes. You can add more sets if you feel like it, or you can add other exercises, this doesn't exclude any other activities you wish to add.

It's just an excellent minimum hygiene-level of physical activity to maintain every day. The more burdensome you make your routine, the more likely you are to say fuck it.

In this context, maxreps means to do as many push-ups as you can in a single set (until your arms give out).

The other commenters haven't said this yet: it's short for "maximum repetitions".