Externalism is the view that the reasons for our beliefs come from sources external to the mental life we have, whether it be nature or some other physical processes that make the beliefs true and reliable. One motivating argument for this view is a challenge to internalism, which is the view that reasons for beliefs come from a person's mental states. The externalist challenges the internalist to explain how we could ever say that very young children and animals have knowledge at all without appealing to reliable processes or mechanisms external to the specific mental states. The externalist charges that the mental states of young children and animals are not sufficiently complex for them to have reasons for their beliefs. So, it follows, externalism is true.
Another argument for externalism is that what we are looking for are objective facts or objective probabilities so that we can have a guarantee for knowledge, which is supposed to be objective. The only sources that would be guarantors of objectivity would be external. So, externalism is true.
Taking each argument in turn, the argument about young children and animals relies on the children and animals having mental states complex enough for them to be able to provide reasons for their beliefs, or put another way, they would have to be able to, in principle, generate reasons for their beliefs. I contend that if this were the way mental states were to be construed, then externalism would have a case. But suppose that if 'knowledge' were given a technical sense, it would be a kind of system in the mind/brain that is made up of principles and parameters that allow for operation relative to certain domains (anything from speaking a language to doing biology). If this were what knowledge is, essentially the sum total of all knowledge systems, then a mental state relative to some domain would just be the state in which a person is in at a given time and for which is making use of a knowledge system the person has. These need not be conscious. They could be very abstract.
If this were all true, then the reasons for any given belief could be internal to the mind/brain without being something someone could verbally express or consciously think is a reason for the belief. If for the externalists this is close enough to their appeal to certain reliable objective external processes, then so be it. Then internalism and externalism are not so apart after all. We should be careful about our word choice, though, because sometimes externalism means a mind-world connection that is posited that we could never actually know we had if we had it.
This brings us to the next argument that what we want are objective facts and objective probabilities and an externalist view would provide for this. But given that we cannot escape our own skins, wanting a mind-world connection does not guarantee one. Inasmuch as we reason or do science, we hope we're achieving one. But this hope is something like a leap of faith. Which will have to be good enough. Even so, it could be the case that the whole world is destroyed and we never know it, and all the mental states be exactly as they are.