While I love @Lucas Wojciechowski's answer, I'd also like to answer this from a different direction, as OP is asking about the distance covered in a single day.
I think here the estimate of roughly 20-30 km per day (13-20 miles) is a reasonable base-line assumption given:
- you know you'll be on decent trails without excessive elevation
- you won't waste time on navigation (because of obvious landmarks or good trail signage)
- your goal is to cover ground (i.e. no hours spent fishing, landscape painting, sightseeing, etc...)
This will be sustainable for longer multi-day treks even with reasonable pack weight (15-25kg) and with mediocre stamina & training. Also this assumes that you need to spend time to break camp in the morning, setup camp at night, spend time cooking, collecting/purifying water, getting stuff out of and into your backpacks - in short on an 8-10 hour day you'll hardly do 8-10 hours of actual walking.
--> But, all of this considered, in my experience (of many months and hundreds of kilometers of treks) the 20-30 km/day can be a reasonable assumption to base any route planning on if you want to plan a trek on a well-mainained long-distance hiking trail (e.g. Kungsleden, Appalachian, CDT, Camino de Santiago, ...).[1]
If you ever go off-trail, then all bets are off: as Lucas outlined in his answer, depending on various factors your speed can slow to a crawl. In such situations you either need good beta on the planned route (e.g. from locals, a good guide book, etc.) or you need to plan with very conservative speeds, to ensure they will be sustainable for you and your group.
[1] This is especially true because over multi-day hikes any daily deviations tend to even out over multiple days.