Taut means "tight" or "under tension", as in a rope or bow string.
A spankee's bottom is said to be taut when the position of the legs relative to the torso is bent such that the flesh, fat and skin of the buttocks is stretched and pulled over the underlying pelvis body — for example, in the touching-toes position or in the diaper position.
When taut, the gluteal sulcus disappears due to the stretch. The buttocks are firmer and less 'wobbly' than when relaxed. The firmness of taut buttocks, however, is of a different kind than the firmness of tensed (clenched) buttocks. The stretched gluteal muscles, in fact, can not be tensed, or only with difficulty. Taut buttocks are said to be more sensitive, but why this should be so is never explained. In any case they are physically less 'responsive' to spanks. They can not absorb spanks with a lot of thud well, so a stingy implement might work better.
When a spanking is given over one or two layers of clothing, the clothes will absorb some of the impact — especially with a lightweight, stingy implement such as a switch or cane. This effect can be reduced by pulling the clothes taut over the buttocks.
In the mid-19th to mid-20th century when students used to be caned and switched a lot at school, on their clothed bottoms, some teachers would take a firm grip on the boy's waistband to pull his trousers taut for a spanking. In fact, one of the German idioms for spanking is "die Hosen strammziehen" or "den Hosenboden strammziehen", which means to pull the (seat of the) trousers taut.
When clothes are tight by themselves, pulling them taut is unnecessary.
Drawing by Wilhelm Busch (1860).