Coherentism is the position that a belief is justified if it forms a part of a ‘network’ of beliefs which are sufficiently mutually coherent with one another. Unlike foundationalists, who believe that all justifications eventually ‘bottom out’ in some fairly small set of fundamental beliefs which require no further justification, coherentists argue that beliefs are connected to each other in a complex, intertwined web of justifications which indirectly links together all of our beliefs in a coherent structure. Although there are differing accounts as to exactly how to understand ‘coherence’, usually it is understood to mean a combination of consistency, degree of mutual support, and explanatory power. Coherent systems of beliefs are thus internally consistent, fit together well in mutually justifying relationships, and can provide a framework to understand or explain a wide range of things.
In addition to difficulties in articulating exactly what is meant by the notion of ‘coherence’, coherentists also face the challenge of explaining how it can rule out systems of beliefs which are coherent but isolated from reality, such as might be found in highly elaborate and coherent, but ultimately fictional universes such as Star Wars or The Lord of the Rings. Finally, coherentists also face the difficulty of accounting for how and why their proposed model of justification is not viciously circular (as in ‘I know something because I know it’) in a manner that renders it incapable of delivering knowledge.
Coherentism: introductory piece from TheoryOfKnowledge.info
Coherentism in epistemology: more detailed analysis from the Internet Encyclopedia of Philosophy
Coherentist theories of epistemic justification: a detailed overview of classical and modern approaches to coherentism from the Stanford Encyclopedia of Philosophy