Tadmeen
Tadmeen (تضمين, literally "insertion") is a hypothesis which tries to explain away why the Quran sometimes uses wrong prepositions. The explanation is that if a word is used with a wrong preposition, then it's because a different word which can be used with that preposition, was invisibly inserted into the original word.
English analogy
In English we can say "believe in god" and "pray to god". If the Quran was in English and contained "believe to god", it would be an error, because it should be "believe in god". And one way apologists could try to explain it away would be to say that the word "pray" was invisibly inserted into the word "believe" and since "pray" can be used as "pray to", then "believe to" is also correct.
Examples
Most people read only the translation of the Quran and translators usually "solve" (thus hide) the linguistic problems in the Arabic original. And even Arabs if they notice the problem they might blame their own judgement rather than the Quran. So the only people who really have to deal with this are translators and grammarians and so the issue is not known much.
"They humble themselves to their lord (فأخبتوا إلى ربهم)
The verb أخبت (to humble/submit oneself) is used with the preposition ل. For example:
And so those who were given knowledge may know that it is the truth from your Lord and [therefore] believe in it, and their hearts humbly submit (فتخبت) to it (له, la-hu). And indeed is Allah the Guide of those who have believed to a straight path.
However in 11:23 it's used incorrectly with the preposition إلى:
Indeed, they who have believed and done righteous deeds and humbled themselves to their Lord (فأخبتوا إلى ربهم) - those are the companions of Paradise; they will abide eternally therein.
And the apologist explanation is:
وفي الآية ضُمِّن الفعل (أخبتوا) معنى (أنابوا)، فعدِّي بحرف الجر (إلى)
And in the verse the verb "humble themselves" included "return" so it was used with preposition إلى
So a word which can use that preposition was somehow inserted into it.
"Allah's servants drink with a spring" (عينا يشرب بها عباد الله)
A spring wherefrom (بها, bihaa) the slaves of Allah will drink, causing it to gush forth abundantly.
The word bihaa actually means "with it". It's strange in Arabic to say "drink with a spring". The correct preposition is "from" (من), "drink from it". Ibn Kathir explained it as a case of tadmeen:
ولهذا ضمن يشرب معنى يروى حتى عداه بالباء
The word Yashrabu (to drink) includes (ضمن) the meaning of Yarwa (to quench one's thirst)
The translator of Ibn Kathir didn't translate the final part حتى عداه بالباء, "so that it could be used with with".
So the Quran said يشرب ("drink"), but uses a wrong preposition and that is supposedly caused by the word يروى being invisibly inserted into the word يشرب and since يروى can be used with "with", then "drink with" is also correct.
"Sexual intercourse to your wives" (الرفث إلى نسائكم)
This is 2:187 translated by Muhsin Khan:
It is made lawful for you to have sexual relations (الرفث) with (إلى) your wives on the night of As-Saum (the fasts)..
The word إلى actually means "to". The word "with" would be مع or ب. And it's not correct in Arabic to say الرفث إلى ("sexual intercourse to [someone]") as the Quran says it. ِAnd the apologetic explanation is that it's a case of tadmeen (insertion) [1] and that the word الإفضاء (to go) was inserted into the word الرفث ("sexual intercourse") and since it's correct to say الإفضاء إلى ("go to"), then الرفث إلى ("sexual intercourse to") is also correct.
The translation Sahih International even translates it as "go to" and puts "for sexual relations" in brackets, although in Arabic the verb "go" is not present at all and the word "sexual intercourse" is:
It has been made permissible for you the night preceding fasting to go to your wives [for sexual relations]..
Tadmeen of prepositions themselves
Some scholars also say that not even verbs can me tadmeened, but even the prepositions themselves.
For example:
The preposition "over" supposedly tadmeened the preposition "in" (في), so it's "in the fire".
Or another example:
O you who have believed, when [the adhan] is called for the prayer on (من) the day of Jumu'ah [Friday], then proceed to the remembrance of Allah and leave trade. That is better for you, if you only knew.
The word من actually means "from". And the explanation is that the correct preposition في was invisibly inserted into it.