There could be several things you notice and they’re different.
Taxiing the aircraft happens with the thrust from the engines too, not with a separate engine driving the wheels like many people seem to think. Often there’s no need to add thrust to start rolling for taxi, there will be enough of it when the engines are at idle and the plane will slowly start rolling. But if the aircraft is heavy or if it has to go uphill, thrust may be required to get going or keep the speed above a certain value, say 10 knots.
Why do I mention that? Because you are often standing still at the holding point of the runway, waiting for clearance from Tower to line up on the strip that gets you airborne later. Nobody wants you to take your sweet sweet time to line up, causing more of a traffic jam behind you and causing the British Airways in approach to go around since the runway isn’t clear. Add to that that runways are built with an upslope towards the centerline (to drain water in heavy rain) and you’ll see that often a good amount of thrust is required to just line up the plane on the runway.
Then you often can’t just take off yet. Again, you have to wait until Tower clears you. The controller up there may have to wait for the plane that just landed to get off the runway, or wait until someone landing on another runway won’t go around and become a factor for your takeoff… So you come to a stop again, now neatly lined up. No point in wasting fuel and wearing out brakes by leaving the thrust on then, so you go back to idle until you’re cleared for takeoff.
Once you’re cleared for takeoff, the thrust goes to the takeoff setting in two parts, as other answers have pointed out. You first set a certain low setting to see that the engines spooled up in unison, have a quick check at the instruments to see all is normal, and then go to your desired takeoff setting. Like other answers state, there’s no going back to idle on this one, unless something is wrong.
(The next airplane in the queue for line up is holding in idle. He may soon need a good amount of thrust to line up next, going uphill, without taking his sweet time and upset every one else. The one lined up here just went through the same thrust increase and is now back in idle, waiting for takeoff clearance. Someone may be landing on the other runway, that crosses this one further along.)
Apart from that, there are other things that can happen during taxi and lining up, which are less common.
During taxi in icing conditions some engine types need regular spool-ups to shed possible ice building up in the core or on the fan blades. You may wonder about this when it’s a cold misty day. It’s also common to spool up the engines higher than normal before going to the takeoff thrust setting when there are icing conditions.
Or clearances change. Line up cancelled, takeoff cancelled, different runway than expected, traffic ahead has an issue… all things that may affect the thrust setting of the engine during taxi and lineup.
Because you describe it as “reduces it [the throttle] a bit and then fully accelerates it” I suspect that you refer to the thrust increase of lining up the plane, getting back to idle once lined up, then setting the takeoff thrust (in two stages).
