A belief is a propositional attitude.That is, it can be placed in a general form as a relation between someone and a proposition. So "John believes that the sky is blue" can be rendered as

Believes (John, "The sky is blue")

B(a,p)

There's ill will in some circles towards this sort of analysis. Think of this as setting up a basic structure or grammar for belief. A belief is a relation between an individual and a proposition. That there is much more to be said about belief is not in contention; this is just a place to start. This is set as a falsifiable proposition. If there are any examples of beliefs that cannot be stated as relations between individuals and propositions, this proposal would have to be revisited.

It has been suggested that animal and other non-linguistic beliefs are a falsification of this suggestion. The argument is that non-linguistic creatures can have beliefs and yet cannot express these beliefs as propositions, and that hence beliefs cannot be propositional attitudes. But that is a misreading of what is going on here. Any belief, including that of creatures that cannot speak, can be placed in the form of a propositional attitude by those who can speak. A cat, for example, can believe that its bowl is empty, but cannot put that belief in the form B(a,p).

Belief does not imply truth
One obvious consequence of a belief being a relation between an individual and a proposition is that the truth of the proposition is unrelated to the truth of the belief.

That is, folk can believe things that are untrue. Or not believe things that are true.

A corollary of this is that belief does not stand in opposition to falsehood, but to doubt. Truth goes with falsehood, belief with doubt. And at the extreme end of belief we find certainty. In certainty, doubt is inadmissible.

If belief does not imply truth, and if one holds to the Justified True Belief definition of knowledge, it follows that belief does not imply knowledge.

The individual who has the belief holds that the proposition is true.

This is, if you like, the significance of a belief statement. It follows from Moore's paradox, in which someone is assume to believe something that they hold not to be true. For example:

"I believe the world is flat, but the world is not flat".

While this is difficult to set out as a clear contradiction, there is something deeply unhappy about it. The conclusion is that one thinks that what one believes is indeed true.

Note that Moore's paradox is in the first person. "John believes the world is flat, but the world is not flat" is not paradoxical - John is just wrong. "John believes that the world is flat and John believes the world is not flat" - John is inconsistent.

This perforative paradox comes about only when expressed in the first person.

One might think it so trivial that it is not worth saying: to believe some proposition is to believe that proposition to be true.

That is, talk of belief requires talk of truth.

One might be tempted, perhaps by pragmatism or by Bayesian thoughts, to replace that with measures of probability. You might think yourself only 99.99% certain that the cat is on the mat, and suppose thereby that you have banished truth. But of course, one is also thereby 99.99% certain that "the cat is on the mat" is true.

Belief makes sense of error
Austin talked of words that gain their meaning - use - mostly by being contrasted with their opposite. His example was real.

"it's not a fake; it's real"
"it's not a mirage, it's real!"
It's not a mistake - it's real"

and so on.

Belief can be understood in a similar fashion, as gaining it's usefulness from the contrast between a true belief and a false belief. That is, an important aspect of belief is that sometimes we think that something is the case, and yet it is not.

We bring belief into the discourse in order to make sense of such errors.

Belief is dynamic
Beliefs change over time. It follows that a decent account of belief must be able to account for this dynamism.

Beliefs explain but do not determine actions

Beliefs are used to explain actions. Further, such explanations are causal and sufficient. So if we have appropriate desires and a beliefs we can explain an action.

So, given that John is hungry, and that John believes eating a sandwich will remove his hunger, we have a sufficient causal explanation for why John ate the sandwich.

One may act in ways that are contrary to one's beliefs. A dissident may comply in order to protect herself and her family.

So given that John is hungry, and has a sandwich at hand, it does not follow that John will eat the sandwich.

An individual's belief is inscrutable
One can act in ways contrary to one's beliefs. It's a result of the lack of symmetry between beliefs and actions mentioned above - Beliefs explain but do not determine actions. Thanks due to Hanover and @Cabbage Farmer.

Any belief can be made to account for any action, by adding suitable auxiliary beliefs. — Banno

If you believe something that's true, then it's justified.

If you believe something that's not true, then it's not justified. — flannel jesus

It can't go unnoticed how various people "know" things that contradict what other people "know" as well. Some people know that Jesus is King, other people know Muhammad was the last prophet, other people know Krishna is the eighth avatar of Vishnu. — flannel jesus

Did we falsely think we knew before? — Bylaw

But later we may realize errors or get new data and then we know X is false. — Bylaw

There is no knowledge! — Chet Hawkins

Manne just isn't one on my account — AmadeusD

I had you pegged as an Englishman. — Leontiskos

Not Abbott? — Leontiskos

Peterson always strikes me as a man having a breakdown in slow motion — Tom Storm

His idea (in chapter six of his book) that what leads to mass shootings in general, and school shootings in particular, is a kind of ahistorical, existential angst, or a “crisis of being” — that’s the phrase he uses! — about the despair and misery and suffering of human beings.

Peterson thereby takes on a huge burden of explaining why white women, people of color, nonbinary folks, and so on, almost never act on our existential angst and despair in this way. Because, as you know, the vast majority of school shooters have been white men. — A feminist philosopher makes the case against Jordan Peterson

I think you are right. — Athena

an enthytema often — Lionino

Why would we expect ideological uniformity from over 1000 years of texts? — BitconnectCarlos

Read it and make your own judgments. — BitconnectCarlos

(God) does reveal certain things within the pages of the Bible. — BitconnectCarlos

God is inscrutable in his entirety. — BitconnectCarlos

I'm just saying you truly have not presented any interesting criticism. — Hanover

The positivists were right. Philosophy is nonsense. We should all learn coding instead. — Lionino

woof, woof, growl. — Corvus

give me an real world example — Metaphyzik

That there are green crows implies there are no new ideas. — Banno

The opposite of p->q is of course p->~q — Metaphyzik

This covers it: q -> (p v~p) — Metaphyzik

Now let me ask you an honest question. Can you say what Descartes meant (or gets credit for for some reason even though any idiot knows “I am” for certain)? What did Descartes mean? — Fire Ologist