Speaking of knowing God's Trinitarian nature, one element of the new Mass translation that is not changing is that part of the Creed where we say "one in being with the Father." Or at least that part of the translation will stay the same in the United States--other English speaking countries will use the new (older) "consubstantial with the Father."
What is the difference supposed to be, you may ask yourself. The motivation for keeping the wording the same may be nothing more than the same old banalization of American liturgical English that we've all grown accostomed to since the 1970s. "One in being" is a little easier to grasp, let alone say, than "consubstantial", and our Bishops are rather notorious for thinking that we're all a bunch of morons when it comes to participating in the Mass. But I'm not so sure that there's no difference in meaning between the two phrases.
To say that two things are one in being suggests a kind of identity relation. Hesperus and Phosphorus are one in being because they are really the same thing--the Morning Star is the Evening Star just because the expressions are nothing more than different semantic signs for the same entity, the planet Venus. The expressions have slightly different meanings, of course, since the Morning Star is what we call Venus when we see it in the morning, and the Evening Star is what we call it when we see it in the evening, but they refer to the same object.
But the Son and the Father are not the same object in quite the way that the Morning Star is exactly the same object as the Evening Star. Insofar as the two names pick out objects, those objects have all qualities in common save for the referring expression that we use to name them. That is not the case with the Son and the Father--although they are, in some sense, one, they do not share all the same properties. The Son is begotten, but the Father is not. So they do not participate in the same sort of identity relation that the Morning Star and the Evening Star participate in.
Yet they are one in some sense. The sense in which they are one is that they have the same essential nature. In old-fashioned philosophical jargon the word for an "essential nature" is "substance". I say "old fashioned" because in ordinary modern English usage the word "substance" tends to refer to some material stuff: "What is this substance on my shoe?" "Please fill my glass with some more of that delicious substance!" etc. But in the old scholastic tradition a substance is simply a kind of being, and if you're a scholastic then kinds of beings do not need to be material things. God is a substance, angels are substances, and so on. In the case of substances that are material objects then it is precisely the matter that differentiates one instantiation of the substance from another. One human being and another are idential in terms of their essential nature, humanity, but they differ in respect of the particular matter that they are made out of. Matter is thus the principle of individuation in the case of material objects. Since non-material objects cannot be differentiated in this way they must be differentiated in some other way. Angels, for example, differ from each other in their essential natures--each one has its own specific essence. Angels are, thus, indivudally sui generis, one of a kind.
God also is a non-material substance, and so, if God were like the angels, he would be sui generis, one of a kind; and so he is. And yet we speak of him under three aspects: Father, Son, and Holy Spirit. These are names of the "persons" of the Trinity, and they--strangely--differ from each other not in respect of some material principle but in respect of the relations that exist among them. The Father begets but is not begotten; the Holy Spirit proceeds from the Father, but the Father does not proceed from anything, etc. And yet, because all three Persons are non-material substances, and there is only the one substance common to all three--the one essential nature--they are not like the angels, who differ from one another and are not one. The three Persons of the Godhead are, by virtue of this rather unusual metaphysics, literally one in being in just the way that humanity itself--as opposed to the individual humans who share in it--is one single thing.
But it is a very unusual metaphysics that draws distinctions regarding a sui generis, one of a kind entity in this way. In fact, the Godhead is the only entity of which any of this could possibly be true, otherwise metaphysics itself wouldn't make any sense. The Godhead is a kind of exception to a general metaphysical principle. The Latin term, consubstantialis, used in the traditional Latin translation of the Nicene Creed, probably should be translated as "consubstantial", rather than "one in being", if only to preserve the fact of this truly bizarre feature of our theology. "One in being" is a phrase that is true of lots of things; but "consubstantial" is a word that has always been reserved, so far as I am aware, to this one specific theological usage.