An embedding space is a (typically) high dimensional space that has enough dimensions such that examples of some type of entity (e.g. faces, words, or thoughts) can be represented as points in that space, positioned such that they are nearby to other entities with which they have things in common.
An entity embedding doesn't need to use all the dimensions of the space it is positioned in - some dimensions may be unused (sometimes represented as a coorrdinate of 0 in that dimension). These are called "sparse" embeddings. For example, an LLM's tokens are represented as embeddings in what is typcially an approximately ~1000 dimensional space, but start out as sparse embeddings just representing a short letter sequence (but then go on to be transformed/augmented with additional information and so become less sparse).
As an example, let's say an embedding space has 10 dimensions, then a couple of sparse embedding examples could be:
[0 0 1 0 0 1 1 0 0 0]
[1 1 0 0 0 0 0 1 0 0]
These two embeddings have no overlap (where both are non-zero), and the more dimensions you have the more likely it is that two random sparse embedding will have little in common.
Embeddings are used in many types of artificial neural networks, not just LLMs, for example face recognition networks, where they are trained such that similar faces (multiple photos of the same person) are close together in the embedding space, and post-training you can then "look up" any arbitrary photo (in the training set or not) by embedding it and seeing what is nearby in the embedding space, which will be similar looking faces.
Presumably real neural networks used embeddings in a similar way, since, for example, it obviously requires many neurons to represent the many differences between different faces, and there is going to be overlap between the neurons used to represent multiple faces (this is not a computer with one storage location for face #1, and a different location for face #2).
A neural network, real or artificial, uses groups of neurons (e.g. a cortical column) to represent an embedding space, with each neuron corresponding to a dimension. A single group of neurons (column) can store multiple embeddings (e.g. faces) represented as different activity patterns (which neurons are firing), and if these are sparse embeddings then the firing patterns corresponding to different memories stored in the same column will have little in common.
Now, I don't know how you believe associative recall is implemented in the brain - how does someone's voice, or half obscured face, recall their entire face, so feel free to imagine it as implemented however you will, but I'd suggest that in an assembly such as a cortical column that when a set of synaptic inputs are triggered the assembly as a whole will learn to reactivate the entire pattern when only part of the original set of synaptic inputs are triggered, and this is the basis of associative recall. There are papers that suggest exactly how this may work given the cortical column microcircuit.
So, with all that said, the suggestion I was making for why (or at least one reason why) memory degrades with age, with memories blending together, is that with a finite quantity of "storage" (cortical columns) you will eventually be storing so many memories (absent a deliberate forgetting mechanism) that there will inevitably be overlap between the sparse embedddings, and this associative recall will therefore not cleanly recall individual memories but rather recall blended memories according to what they have in common.
Obviously some types of memory are at least initially stored in the hippocampus, so no reason to focus on cortical columns, but I expect the use of embeddings is universal.