How much of a difference in meaning is there between these three sentences, and are any of them better suited to formal writing than the others?
- They must [do things] before they can begin to understand these concepts.
- They must [do things] before they can understand these concepts.
- They must [do things] before they understand these concepts.
They must [do things] before they can understand these concepts.
This one is probably that which says precisely what you mean without either excess or ambiguity.
They must [do things] before they can begin to understand these concepts.
The begin provides emphasis, but seems a bit needless. I'd use it if I meant it literally. Conversely if I really did want to pile on emphasis (e.g. I was responding to someone who disagreed with the need for [do things]) I'd go all out and use "can even begin to".
They must [do things] before they understand these concepts.
Ambiguous with the idea that the time when they understand the concepts acts as a deadline by which time they must [do things]. It's not a very readily available misreading, so I don't think this ambiguity is a major problem, but it's enough to make me lean against it.
are any of them better suited to formal writing than the others?
I'd favour the second in any register.
My "can even begin to" alternative (again, only suitable if I've a strong reason for such emphasis) I'd be less likely to use the more formal I wanted to be; not ruling it out in any register, but the more formally I was writing the more I'd only do so when opposed to another opinion.
The word can as used in your sentences is equivalent to saying:
..before it is possible for them to understand these concepts.
Without the use of can, it means that they must [do things] before they will understand these concepts.
I suggest number 2 in the most formal contexts. Number 1 isn't exactly infrmal but it might be excessively rhetorical in tone. Number 3 has a somewhat different implication, which in a formal context might be picked up on, whereas in an informal context it might be overlooked.
They must [do things] before they can begin to understand these concepts.
= It is impossible to start the process of understanding the concepts until they have done these things.
They must [do things] before they can understand these concepts.
= It is impossible to completely understand the concepts until they have done these things.
They must [do things] before they understand these concepts.
= (Literally) It is in theory possible to completely understand the concepts before they do these things but they are nevertheless obliged to do them first.
