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While reading about 'defective verbs' on Wikipedia, I came across this term – preterite present verbs.

The most commonly recognized defective verbs in English are auxiliary verbs — the class of preterite-present verbs — can/could, may/might, shall/should, must, ought to, and will/would (which was not historically in Old English a preterite-present but has joined the class in modern English) [Source]

The so-called preterite-present verbs are a small group of anomalous verbs in the Germanic languages in which the present tense shows the form of the strong preterite, and the preterite is weak. [Source]

I understand why modal auxiliaries are referred to as 'defective verbs' as far as their incomplete conjugation (lacking an infinitive, future tense, participle, imperative, and gerund) is concerned. But I do not understand why they are also referred to as 'preterite present verbs'.

'Preterite' expresses a past action or state, but how is that sense applicable to all modal auxiliaries? I don't see how can, will, may and shall express a past action or state.

The extent to which we can still call these preterite-present, is that they have present-tense uses for the past tense form. For example, while we can use could as a straight-forward enough (if irregularly formed) past tense of can in a sentence like:

I could run that far when I was younger, but I can't any more.

We can also use could in the present tense.

I could run that far when I was younger, but I *could*n't any more.

Including in forms where we must use could, and can wouldn't serve:

I could really do with a coffee right now.

Remember, that can and could are forms of the same word. You said "I don't see how can, will, may and shall express a past action or state", and the answer is rather than the past tense of those words—could, would, might & should can apply to the present tense.

Now for the history bit!

In Old English there were two main forms of verb; strong and weak. They differed in terms of how they were inflected for person, tense, number and mood. Indeed, we still have the legacy of this in Modern English, so some people still use the terms for Modern English.

A weak verb would change tense by having a set ending added to it. This is the case with most Modern English verbs (walk → walked, watch → watched, auction → auctioned).

A strong verb would have a change in vowel to change tense and sometimes mood. This is still the case of some of the Modern English equivalents (ring → rang/rung, bite → bit/bitten, come → came, shake → shook/shaken).

Because there are relatively few strong verbs in Modern English, many people don't use the terms weak and strong about Modern English, but just regular and irregular, considering all the remaining strong verbs as special cases.

The two also differed in how number and person worked with each type. There was a third class that would act like the strong for the past tense and the weak in the present tense, in this regard.

The fourth class were the preterite-present verbs, where a form you would normally have with a strong past tense, was used in the present tense, and then the other inflections were done as if they were weak. So for this reason, they had some qualities of past-tense verbs when they were in the present. Hence the contradictory name preterite-present.

Old English had many more preterite-present verbs than Modern English. The only remnants in Modern English are the auxiliaries. This was not the case in Old English in both directions; by which I mean that not only where many other verbs preterite-present, but that the auxiliaries weren't auxiliaries in Old English (they also weren't defective, you could say sculan in Old English while the closest translation "to shall" or "to should" isn't correct Modern English.

Willan was neither defective, nor preterite-present, though the modern will/would is both. It was a strong verb.

"Preterite-present" doesn't mean that can, will, may and shall "express a past action or state".

It is just a term used to describe a category of Germanic verbs that originally showed a certain pattern of inflection. (Similar to the terms "strong" and "weak" verbs.)

The basis of the categorization isn't the meaning of the verbs, but the form that they take in the present tense. (The meaning may have played a factor in these verbs originally developing these special forms, and it may have affected which ones retained them, but the term "preterite-present" isn't directly about meaning.)
Like a past-tense verb, the word may doesn't take the third-person singular suffix in the present tense. We say he/she it may, not he/she/it *mays. This is also true for the ancestors of the word: according to Wiktionary, the third-person singular present-tense form of magan in Old English was mæġ, and the third-person singular present-tense form of the reconstructed Proto-Germanic verb *maganą is *mag.

I don't like the wording of the sentence "will/would [...] has joined the class in modern English", as John Lawler says in a comment, it makes more sense to refer to the category of modern English verbs that don't inflect as "Modal Auxiliary Verbs".