There are 2 chainrings in the front, 8 speed cassette in the back. On this bike, using the big ring in front and small ring in back feels sluggish, like I'm wasting energy and not getting much in return. With my other bikes, that combination gives me some good speed. When will I want to use the big ring in front, small ring in back?

For most amateurs, only when going downhill...every once in a while you might be going fast enough on a flat, in a group, but for me, even in the low to mid 20's mph...I'm a few cogs away from the smallest.

If this bike has an 11 tooth cog, and your others had a 12 or 13 as the smallest, that would make a difference too...

When climbing the L'Angliru or other easy mountain road.

Think of the big front chainring as "High range", and the small front chainring as "low range" (although there is some overlap)

"High range" is for downhill, or flat roads with a tail wind.
"Low range" is for uphill, or flat roads with a head wind.

When drafting (vehicles or other riders) or on an all out sprint. I used my largest gearing only a handful of times keeping up with the flow of traffic while catching the slipstream from a large truck or bus.

So it's unlikely or rarely that one will use an 11 or 12 tooth cog in back, so aren't 6 speeds enough? Most of my "freewheels" start with a 14, and I rarely use it. Even when racing my top gear was a 49/14. Why so many big gears on bikes these days?

when taking pictures for the internets

1: down hills

2: when wandering into the pain cave

Because big gears are cool, even though rarely needed.
The advantage of more gears is to have smaller steps between gears, so you can more easily find the "right" gear for any given situation.
Each person having the appropriate high and low gear for them, means that they can make use of them all. Having a ridiculously high or low gear is just a waste.

Because they're faster. You think Eddy Merckx wouldn't have used a 53/11 had one been available?

And the reason 6 speeds aren't enough has little to do with the range of gears, it is that 10 or 11 speeds allow much smaller steps between gears. More efficient and actually a good deal more pleasant to ride than my old six speed.

EDIT I see homebrew has beaten me to it.

Range has something to do with it. How many guys would be running an 11-28 or 11-32 on the road if it weren't for 11 speed cassettes? I tried an 11-32 9 speed on the road a few years ago and hated it. With 11 speed, I can have virtually the same spacing as my current 12-27 9 speed cassette but get those two lower gears as well.

I didn't know that other gears existed? When don't you run the 53-11?

Yeah, OK, but the advantage of the 10 or 11 speed isn't that you can have a bigger range, it is that the close ratios mean you can have the big range without the crappy spacing. We're making the same point.

Ironic username...

When you need to drope the hamar and dial it up to 400 with your 54-10!

The 12-25 11 speed cassette I'm going to be putting on my latest build is going to make any other cassette I currently run feel like crappy spacing. But, yeah, we're basically making the same point.

+1

Yesterday I struggled to reach double digit speeds in the granny gear for 15 miles into a 15 MPH sustained wind. When I turned around I used the Big/Small combo. Hit 40 MPH at one point. Zooooom!

No. One tooth jumps feel good through about the 19 cog, and with a 39 small ring needed to delay shifting you need 9 or 10 to get to 14-25/26 or 13-25/26 with a low gear adequate for mountains so you can use the same cogs for climbing and plains rides.

Most people buying bikes can't be bothered with learning to pedal fast.