It would seem that there are 2 questions here:

(1) How can you pray Ma'ariv when it is still light outside?

(2) How can you read the night Shema when it is still light outside?

(1) The Gemara (below 26b) states that Rebbi Yehudah maintains that one can only Daven Mincha until Plag because the evening Tamid sacrifice was only brought until Plag. Tosfos DH Ad writes that Rebbi Yehudah maintains that the prayers were instituted to correspond to when the incense was offered in the Beis ha'Mikdash as is said (Tehilim 141:2) "May my prayer be acceptable before You like incense; the lifting up of my hands for the evening offering". In fact the source for Tosfos' statement is the Talmud Yerushalmi 4:1 (p.60) which states that Minchah according to Rebbi Yehudah does not actually correspond to the Tamid but rather to the incense which was only burnt until 1 and 1/4 hours before nightfall. The Meleches Shlomo on the Mishnayos writes that it is not clear to him how Tosfos knows that the incense was only burnt until Plag. However he also writes that it may be that the "evening offering" mentioned in Tehilim refers to the Arvit night prayer. If we accept that the incense was only burnt up to Plag (see commentaries on Yerushalmi) it seems to me that this suggests that once the time of Minchah has finished it automatically follows that the time of the "evening offering" i.e. Arvit prayer, starts.

In short, since in the Beis Hamikdash the time of Arvit started at Plag, we also can say Arvit from Plag onwards according to Rebbi Yehudah even though it is somewhat light outside.

(2) The Torah commands us to read the Shema "when you lie down to sleep and when you arise" (Devarim 6:7). The Rishonim in our Sugya write that the time of reading Shema does not depend on night but rather on when people go to sleep (see the Shitah Mekubetzes 2b DH v'Inhu and the Meiri 2a DH ha'Mishnah and note 3 there). Tosfos 2a DH Me'eimasai cites Rabeinu Tam who maintains that the Halachah follows Rebbi Yehudah according to whom one does not have to say Shema again at home (unlike Rashi). Rabbeinu Tam maintains that Shekiyah is 72 minutes before Tzeis. Since Plag is 75 minutes before Tzeis this means that Plag is only 3 minutes before sunset. So it is not very light outside at all when he reads Shema. It is possible that since some people do go to sleep at this time (don't forget that before the invention of electricity people went to bed early), this can be compared to what Rebbi Yehoshua said in the Mishnah below (9b) that one can read Shema up to 3 hours into the morning because kings get up at this time. Similarly we follow the minority of people who go to bed after Plag, in order to term this "the time of lying in bed".

(However the Meiri 2a DH ha'Mishnah writes that before 3 medium stars come out noone goes to bed. It could be that Rabbeinu Tam disagrees with this and maintains that there are a minority of people who go to bed very shortly before sunset and this is sufficient to be called "the time of lying down". This matter requires further study).

KOL TUV

Dovid Bloom