Our experience of reality is made by the mind. We don't experience the world directly, instead our mind builds models - and this is what we experience, assuming that to be reality. You would think our models are more or less accurate except some small details - but no, not at all. They are like flat 2D cross-sections of the multi-dimensional reality. They are not just simplifications, they are more like schematics, like wire-frames.
What we habitually assume to be solid entities are mind-made wire-frames. Buddhism teaches that all entities are not solid (we say they are "coreless" or "empty" - shunya). What does this mean?
If you don't think of objects point-in-time, but watch the whole thing over time, you'll see that what you assume to be entities are really just temporary arrangements of various parts set in motion by chains of causes. So entities are just point in time assemblies of trajectories of causes traversing space-time. In addition to causes, there are also ambient conditions necessary for existence of certain entities: pressure, gravity, electromagnetic field, temperature etc. All of these: parts, causes that got them together at this place and time and ambient conditions that keep them together for now - is what we call components of objects. All objects are compound aggregates of components. Traditional term for this is Pali sankharo (Sanksrit samskara) - literally "co-made", made-up by many constituents.
If you think about the above really well, you may realize that the threads of causation I describe above are not really linear. Instead, there is a network of causes and conditions, infinitely forking, joining, and interacting. Depending on the level of observation and on the context the mind will delineate different entities. You are familiar with physical, chemical, biological, electromagnetic, informational levels of observation. These are all different ways to see the same reality. So your experience of entities always depends on you, the observer - providing the level and context, making the delineation, making the interpretation. And what are you, the observer? It is also a temporary arrangement of factors (physical, biological, social, informational etc.)! So what happens in the moment when experience of so-called reality takes place, is that many factors come together to create the so-called "external"/"objective" and the so-called "internal"/"subjective" components of the experience. So what we perceive as objects or entities at the moment the experience takes place are temporary arrangements of physical factors, assembled into a coherent experience by temporary arrangements of mental (experiential) factors - which themselves are temporary arrangements of factors! Actually, physical factors and mental/informational factors are not two different types of factors, they are two sides of the same coin. We say, "form is emptiness and emptiness is form". Nothing solid to rely on at all! This situation is known as "Emptiness" (Shunya-ta).
Besides physical objects, let's not forget that our lives are full of entities of other kind: abstract concepts. Do you know how many times people killed each other because of disagreement about the concepts? And yet, very few seem to realize the obvious: that abstract concepts don't and can never have well-defined meaning. They are just labels that make sense in relation to other labels that we arbitrarily designate. So concepts, ideas are not solid either. They have different meaning depending on context and on who uses it and for what. These dependencies of the concepts serve the role equivalent to the role of causes and conditions that physical objects depend on. We say that both so-called physical objects as well as concepts are both "compound" or "conditioned" phenomena (sankharas) - they are aggregates of factors, with label (nama - name) stamped on top.
One of such entities is "I" - we assume there is something stable, but there is no such thing - only factors, only trajectories, only forces interacting. There is no "internal" vs "external" world (that this separation is a mind-made fiction is proven by the fact that your "internal" is "external" for me). Objectively, there is no "internal" vs "external" - only an infinite field of interacting factors.
Unfortunately most people assume all types of entities (objects, groups, concepts, "I", etc.) to have solid identity that can be relied on (traditional term for this is "existence-by-itself" - svabhava). Not just assume, they insist that their delineation/interpretation of entities is the reality. This is what the sutra calls attaching to external & internal objects" and "attaching to names (concepts, labels, identities)".
