As already source by Noach miFrankfurt in his answer, the German Minhag and likely original minhag Ashkenaz, was only to hold the front corners. This is also the practice of the Vilna Gaon (as recorded in the siddur Eizor Eliyahu), because he strongly felt that it was important for tzitzis to be worn with two of them in front and two in back.
The Shulchan Arukh says only take 2 tzitziyos. (Orakh Chaim 25:5. In the Beis Yoseif the author of the Shulchan Arukh cites the Hagahos Maimon end of ch. 3. The Beis Yoseif also mentions that the Avudraham considers the whole practice of holding tzitzis during Shema to be yuharah, an egotistical holier-than-thou, but only because the masses don't do it. And therefore the Avudraham's ruling would not invalidate following a general minhag to do so.)
As for meaning... The SA explains that brings 16 string and 10 knots visible, corresponding to the gematria of the tetragrammaton (10 + 5 + 6 + 5 = 26 = 16 + 10). The Magen Avraham ad loc says the 10 knots correspond to the 10 Sefiros.
The Kaf haChaim (ad loc #8) explains this custom is to hold the font tzitzios in the left hand, as it's closer to the heart. He also mentions the position of the Ari, that one takes all four corners in both hands.
The Levush (#2) speaks of holding "the tzitzis" in one's left hand, next to the heart. This rather authoritative decisor who tends to give weight to accepted Ashkenazi rulings of his era is a bit ambiguous. "The tzitzis" would seem to mean all four; but as we saw in the Kaf haChaim, the left hand is more the two string practice.
The Arukh haShulchan (who started before the Mishnah Berurah, but wrote Orach Chaim later) also says "the tzitzis", and says one takes them in the left hand, but holds them in both when getting ready to kiss them for Shema. (#3) In the Be'eir Heiteiv, the Mishnah Berurah appears to rule similarly. So, both of the major codes written at the end of pre-War East European Jewry rule like the Ari -- 4 tzitzis, both hands, at least while kissing if not the whole time.
Getting to contemporary rulings: R Herschel Shachter rules one should follow the Shulchan Arukh and only use two. (But then, his Brisker background makes it more likely he would rule like the Vilna Gaon than the more common East European custom.)