Any commentator on 17th- or 18th-century philosophy is likely to have problems with the concept of an 'idea', which is many-ways ambiguous - often in the same writer.
In the Meditations Descartes distinguishes three kinds of ideas:
1.Innate (ideae innatae)
2.Adventitious (ideae adventitiae)
3.Invented by myself (a me ipso factae)
In Descartes' view the idea of God is innate. He believes that we imperfect beings are unable to acquire the idea of God adventitiously or invention. So, Descartes concludes, the idea of God is intrinsic to the human mind.
Adventitious ideas are occurrences such as sounds or my hearing a sound, occurrences which we just happen to experience, to perceive.
A me ipso factae ideas are fantasies which I contrive - the idea of sirens, hippogriffs and so forth, any idea that I can make up.
Hume accepts in his own terminology adventitious and invented ideas. What he does not accept, and rejects absolutely, are innate ideas.
To start from basics, the building blocks of experience are impressions. My seeing a dog is an impression, so is my seeming to see a dog, and so the appearance of a dog to me. Whatever impinges on the senses - whatever is a product of the operation of sensation - is an impression. Ideas are copies of impressions in the wide and general sense that if I see a dog (impression) my recollection or memory-image of the dog is an idea. Any idea is resoluble to the impression(s) from which it derives even though it is typical of ideas that they lack the 'force and vivacity' - the detail and determinateness - of their corresponding impressions.
Hume and belief
Belief formation is brought about by the association of ideas. If, for instance, I have an unbroken succession of similar or identical impressions as of a statue for a protracted period, I will probably believe that I am seeing a continuant, viz. a statue.
I do not experience continuity but in recollecting as ideas the succession of similar or identical impressions, I associate my ideas to form the belief that I have been looking at a continuant.
Hume and education
I am unable to find any connected, extended discussion by Hume on education but it is clear that, to take the example of causation, while the mind 'naturally' believes that A causes B when (a) A is prior in time to B; (b) A and B are contiguous (close in space and time); and (c) A-type events are followed by B-type events with an exceptionless regularity (constant conjunction), we may be induced by false education to believe that a certain constant conjunction obtains when in fact it does not. Equally a sound education will induce correct beliefs.
Inductive inference for Hume is a natural operation of the mind. We do infer the future from the past, the unknown from the known; and much belief-formation (including that involved in education) comes about in this way. Hume's only point is that this natural operation is without rational, non-circular justification. He does not bid us refrain from it. It is a propensity inbuilt in human nature.
'The importance of education as the concept behind the origin of ideas'
Plato's account of education in the Republic and Rousseau's in Emile are of relevant. These at any rate are the first names that come to mind. I'd add J.F. Herbart, however : details are easily available online: https://en.wikipedia.org/wiki/Johann_Friedrich_Herbart.
The Philosophical Writings of Descartes, ed. J. Cottingham et al., Cambridge: CUP, 2008, Meditation III: 26.
Hume, A Treatise of Human Nature, 1739-40, I. III. vii, viii, xi.
Michael Hodges and John Lachs, 'Hume on Belief', The Review of Metaphysics, Vol. 30, No. 1 (Sep., 1976), pp. 3-18.
Henry W. Sams, 'Reflection', The Philosophical Review, Vol. 52, No. 4 (Jul., 1943), pp. 400-408: 403.