"Be" is the prefix meaning "in," so the word we are concerned about is "emet."
There is a play on the Hebrew aleph-bet that illustrates this word and its opposite. "Emet" means "truth." Its opposite is "sheker," which means "lie." Emet is spelled with the first, middle and last letters of the aleph-bet, illustrating that truth can be found anywhere you are, anywhere you look. Sheker is spelled with the last three letters of the aleph-bet – all bunched up at the end. The person who offers a lie finds himself jammed up when he runs out of diversions from the truth.
But truth can be an elusive thing sometimes. Even ignoring Stephen Colbert's notion of "truthiness," something that has an element of truth in it, and even ignoring whether it is always advisable to tell the truth, the whole truth and nothing but the truth (the Talmud urges some latitude when praising a bride, for example), what exactly makes up the truth?
By the way, it is irrelevant to the question whether you believe as some Greek philosophers did that there is a an objective thing called Truth that is independent of context, or whether you believe what is more usual these days that truth is relative to context. When we use the word in prayer and in the deliberation of our sacred texts, truth is a matter of personal integrity more than anything else. In the immediate context of this prayer, it stands alone, but if you think about the Sh'ma, which is sealed with the word "emet," we clarify what we mean by truth immediately. In evening prayers, "emet" is paired with "emunah," meaning faithful or believable. Truth is that in which we can have faith, that which we can expect to believe. In morning prayers, "emet" is followed by a series of adjectives — yatziv, nakhon, kayam, yashar, ne'eman, ahuv, chaviv, nechmad, na'im, nora, adir, m'tukan, m'kubal, tov and yafeh. Never mind what all of them mean; the idea is that any way you look at it, the truth is consistent and reliable. It is completely integrated into the matter at hand, and that is why it is a reflection of personal integrity.
And that is why what makes up the truth is that which can stand up to scrutiny in the bright light. It is no small thing that when we add the word "emet" to the end of the Sh'ma we are proclaiming, to use the translation of Rabbi Zalman Schachter-Shalomi, "adonai eloheikem emet," "your God is the true God." Truth is what we would be unconcerned about associating with the very nature of God.
Our prayer book translates "be'emet" as "faithfully." Associating God and truth makes that a reasonable translation. But just as accurate would be the modern Israeli usage of "be'emet," which serves the same purpose in Hebrew as "no kidding" (in all its variations and intonations) plays in English. And that's the truth. Be'emet.