Today's word, refero, is a compound of the verb fero. It has the same irregular set of parts as the root verb: referō, referre, retulī (you can also see rettulī) and relātus. Both the present stem and the participle are highly productive in English: refer, reference, referendum, etc., and also relate, relation, etc.
The basic meaning is to carry back, to bring back. I really like the frequent use with the word pedes, feet, as in this item from Cicero: me referunt pedes in Tusculanum, (my) feet bring me back to Tusculanum (near modern Frascati).
There is also a reflexive use, meaning to go back, return (i.e. return oneself): Romam se rettulit (he returned to Rome) for example, and me domum refero (I go back home).
It is also commonly used to mean to "report" on something, to bring back news or or intelligence about something as in this example from Aeneid IV: tales miserrima fletus Fertque refertque soror.
From this communicative usage comes the meaning of "reply" or "say in response to something" - e.g., ego tibi refero, I reply to you, I answer you.
Here are some proverbs using forms of the verb refero:
Par pari refertur.
E relato referre fere mentiri est.
Naturale est manum saepius ad id referre, quod dolet.
O mihi praeteritos referat si Iuppiter annos!
Nullum officium referenda gratia magis necessarium est.
Beneficium non esse conferendum nec in puerum nec in senem: in hunc, quia perit antequam gratiae referendae detur oportunitas, in illum quia non meminit.
Also, you need to be aware of a potentially confusing idiom that can LOOK like refero, but is not: mea refert, "it is my business, it concerns me." This is actually a contraction of mea re-fert, where the "re" is not the verbal prefix re- that you see in refero; it is instead the noun res. You can also negate the phrase: Mea minime refert, "It's not any of my business!" Here are some proverbs using this other sense of refero, where the re- is from res:
Tua quod nihil refert, ne cures.
Non quid detur refert, sed qua mente.
Quam bene vivas refert, non quam diu.
Nihil mea refert utrum dives sim aut pauper.
Non tam refert unde natus sis, sed qui sis.
Non quam diu, sed quam bene acta sit vita refert.
Non refert quam multos, sed quam bonos libros habeas ac legas.