The harmonic backdrop is an attribute of a song or any series of notes played over time. It represents the notes which have been played while weighting them based on how many times they have been played.
For this to make sense, we'll make it concrete, let's say we have an anchor note of 3* and we use the anchor intervals 0 2 3 5 7 8 10 (so Eb minor) then if the song was said to be in this key. Then it would mean that the chords in the background (aka the harmony) would most likely be using these anchor intervals.
These anchor intervals are the harmonic backdrop and we can use this information to our advantage when we learn about improvisation later on, that being that when you only use notes which come from this backdrop, then the notes you play will match the background creating a resting feeling, if you don't play the same ones then it would be called "outside" and has its own feelings associated with it.
If someone told you that they were not playing in any key then you could start a count for each note they played and then see which notes they played the most, these notes would create the harmonic backdrop, so as you can see the harmonic backdrop doesn't even need to be a key.
Additionally the harmonic backdrop may change during a song, but the harmonic backdrop is not at the level of chord changes, but at the level of what the key is or what the main notes (or anchor intervals) are which is defined by how many times the notes have been played in total.