I love this term! I like the analogy with the construction of a building because it makes pretty clear what is scaffolding to education.
For me there is a process before, during and after the scaffolding.
Before setting up the scaffolding, a person needs to make sure the ground is clear so the scaffolding is stable. When teaching, we need to make sure distractions are null, we need to make sure the conditions are appropriate to start a new lesson. We also need to make sure that if we need to go to the next step, the first one is strong enough and will serve as a support, otherwise the second step will be so weak and most likely ephemeral.
While working on the scaffolding, we either make sure we have everything we need, or there is somebody close by that can help providing what we need. It´s impossible for a teacher to have all the answers, and it would be ideal if we are smart enough to ask for help and bring to the building somebody with the experience on the subjects that we are not experts. The students will learn that they are not alone and that learning is a social activity.
At one point we need to remove the scaffolding to present the amazing construction we have accomplishesd. When learning, little by little I need the reference points less because I have master a concept. I relate this a lot to language learning. We usually relate a new word to some particular situation and those references are with us for a long time until we take the risk to use the word in a different context, without those old references, then we have learnt the word and we are able to build a new sentence and communicate better.