Externalism in epistemology is the belief that knowledge can be defined in terms of proper function. Proper function involves third person descriptions of how the knower is operating. For instance, whether or not a person knows there is a blue glass on the table depends on the lighting in the room, how well the person's eyes and brain are functioning, that the person is not intoxicated etc. Fallibilist versions of externalism note that all such knowledge claims are open to revision in the future.
Internalism in epistemology is the belief that knowledge is defined as a true, justified belief. That a person thinks a belief is true, and the justification a person gives for that truth, are things "accessible" to the person in a way that functionality properties may not be. Thus, internalism involves a first person account of whether knowledge is present or only appears to be present.
Internalism has come under attack as a failed Enlightenment project. One example is the Gettier problem, traced to an article from 1963 by Edmund Gettier. In this article Gettier gives examples of persons who have what appears to be a true, justified belief but do not have knowledge. However, in each of these examples the justification given is not strong justification, but is a weak example of justification such as testimony from another person. Even though this is an obvious problem for Gettier examples, they have come to be viewed by some as having demonstrated that knowledge must be more than true, justified belief. Indeed, one professor of mine during graduate school said that the only thing philosopher has proven is that Gettier was right about knowledge.
One philosopher who offers an objection to internalism is Michael Bergmann. His objection amounts to a dilemma saying that the justification required by internalism involves an infinite regress or an arbitrary stopping point. One must justify one's justification, and justify that, to infinity, or simply stop at some point and no longer give justification.
The response to this objection is that the stopping point need not be arbitrary. To claim that all stopping points are arbitrary amounts to saying that there is nothing transcendental, nothing that is authoritative and self-attesting. However, his dilemma relies on the authority of reason (as the laws of thought, such as identity, excluded middle, and non-contradiction). A dilemma is only a dilemma if the law of excluded middle has authority. As a student of mine, Andrew Presnell, pointed out: If reason as the laws of thought is not authoritative then we need not listen to Bergmann's argument; If reason as the laws of thought is authoritative then something is transcendental and we need not listen to Bergmann's argument. Either way, Bergmann's argument against internalism fails. Bergmann assumes the authority of reason. Indeed, any meaningful belief or argument assumes the authority of reason.
Some might say that this is a simplistic presentation (I've linked Bergmann's article so it can be read directly), however I believe it is sufficient. We might speak about conscious awareness rather than justification but this does not change the problem Bergmann will face. In other words, the knower must be consciously aware of what grounds his belief, and consciously aware of what grounds that, to infinity. I've used the term justification instead.
Externalists think of knowledge in terms of "common sense beliefs" given their historical situation in analytic philosophy and the ordinary language tradition. These kinds of beliefs are about the color of an object in the room, or what I had for breakfast, or the date of my birthday. These are beliefs from the senses, or memory, or tradition. An internalist account might struggle to give a "simple solution" that shows these are known with certainty. Indeed, I don't see a problem is allowing that these are not known with certainty. Rather, what must be clear is what is most basic. These beliefs are not basic but have many assumptions. If anything is clear it must be the most basic things. That less basic beliefs about the senses, memory, or tradition are not certain does not threaten our ability to know with certainty what is most basic.
Alvin Plantinga has made an externalist defense of belief in God popular. Relying on an analogy to belief in other minds, Plantinga uses the term "warrant" instead of "justification" to say that belief in God is warranted in the same way that belief in other minds is warranted. He argues that belief in God is the product of proper functioning according to a design plan aimed at truth. Of course, to import the phrase "design plan" is to import "God" as the designer into the definition, and therefore the definition becomes circular: belief in God is warranted because it is due to proper function according to God's plan aimed at truth. It is worth noting that Plantinga's argument against naturalism corrects this problem by leaving externalism and instead using an internalist argument to say that naturalism cannot be true.
Indeed, this is a serious problem for externalism: any defense of an externalist theory relies on internalist justification. Internalism, and the need for justification, cannot be avoided. The Gettier problem should motivate philosophers to explore stronger justification, rather than abandoning justification altogether. This is especially true with respect to basic beliefs about which we must be certain.
In this sense extreme forms of externalism are forms of skepticism. Like other kinds of skepticism, it denies that I can have certainty about questions like "how do I know," "what is real," and "what is the good." Like other forms of skepticism, it redefines the word "know" into a something that really means we cannot know. Historically, these seem to go hand-in-hand with naturalist views of human nature and materialist descriptions of the world. Marx and Freud employ externalist accounts of human knowledge, reducing knowledge to physical considerations like economic and social status.
At the basic level, less extreme forms of externalism collapse with internalism. If I am trying to settle a question I will rely on the laws of thought. From the internal perspective this provides knowledge. An externalist description of this would similarly describe my use of the laws of thought. At this level these are only different in perspective (1st or 3rd person) but not content.
Insofar as skepticism, consistently held, leads to lack of meaning, we must abandon extreme forms of externalism.