The campaign messages are really targeted to women of childbearing age, which ranges from teens all the way through the 30s.
I found that the word 'really' here might be interpreted in different ways, such as (copied from Macmillan English Dictionary):
1) very / very much
some really useful information
I really enjoy working with young people.
It seems incorrect here to substitute 'very' for 'really' in the sentence in question
2) for saying what is true used for talking about what is in fact true, especially when something else seems to be true:
We never know what really happened.
Everyone seems to have admired Diana, but what was she really like as a person?
In this case, I have to assume the speaker knows someone who wrongly believes that the campaign messages are targeted not to childbearing women, but to someone else. So the speaker feels a need to make it clear that they are targeted to those women.
3) for emphasis used for emphasizing what you are saying about a situation:
We should really get started. it's already 10:00.
There's really no need to worry.
I really ought to have called Annie to let her know we'll be late.
From these examples, it seems that this sense is used primarily in imperatives or when making suggestions. But that sentence in question is merely describing the situation.
4) completely [usually in negatives or questions] completely:
Rigby had never really recovered from his knee injury.
Are you really sure that you want to marry this man?
It isn't really a dictionary - it's a sort of phrase book.
It just doesn't feel like this sense could apply.
Could anyone please help me understand what exactly does 'really' mean here? I really appreciate that (sense 1 seems to be the relevant one here)
I would say it is likely to mean 'in fact' here.