Let’s take a simple example. Let’s assume you believe that copper is a metal. If you do, then that means you have the concept copper. But what does your having that concept depend on? This is where externalism and internal/ism disagree. According to externalism, your having the concept copper depends essentially on your having been related in the right kind of way to copper itself (you’ve probably read about it, people have talked to you about it, you may have seen things made from it, and so on). And if there had been no copper around anywhere, then, according to the externalist, you couldn’t have possessed the concept copper. After all, how could you have acquired it? Internalists disagree. Internalists think that you could still have possessed the concept copper even if there hadn’t been any around, so long as your brain was in the right kind of state.
Another difference is that externalists think of concepts as public rather than private. You and I both have the concept copper, and both believe that copper is a metal, but we may have somewhat different understandings of what copper is – we may have different beliefs about how well it conducts electricity, or how malleable it is, and so on, but it’s still copper we’re thinking about because of our causal connections to it. I think it’s clear that people have slightly different surrounding beliefs about most things most of the time, but I don’t think that means we can’t all think about the same things. Externalism explains how this is possible.
In short, if externalism is true, an individual’s mental states (her beliefs, desires, fears, hopes, imaginings, and so on) are not determined entirely by her internal, physical states (her brain states, for instance). Rather, they are determined by her internal, physical states together with her relations to an external environment. But if mental states are not determined entirely by brain states, then the mind cannot be identical to the brain. This goes against a common view according to which the mind is, in fact, just the brain. If externalism is true, then minds are not just brains.
It also means that you can be a non-reductive materialist without being a physicalist.
Externalists can accept materialism, but reject physicalism.