The Torah tells us that Bnei Yisroel left Mitzrayim in a hurry and did not even prepare any provisions for the way. Rashi (Shemos 12, 39) comments that from here we see Bnei Yisroel's greatness; they followed Hashem into the wilderness without an inkling of where they would procure food for themselves. Referring to this occasion, Hashem declared, "I recall for you the kindness of your youth, the love of your nuptials, your following Me into the desert, into an unsown land." Rashi adds that the reward for this blind faith is mentioned in the following pasuk, "Yisroel is holy to Hashem."
Rav Wolbe (Shiurei Chumash) says that it appears from the pasuk that because Bnei Yisroel had bitachon they were rewarded with kedusha (becoming holy). We tend to think that bitachon and kedusha are two concepts that are entirely unrelated. However, the Navi is enlightening us to the fact that these two middos are interdependent, and Bnei Yisroel merited becoming holy due to their complete bitachon in Hashem.
We can explain the connection between bitachon and kedusha as follows. Kedusha means to be devoted in an absolute manner. Hence, the Torah refers to one who is dedicated entirely to Hashem as a kadosh, while a man who is devoted to promiscuous activity is referred to as a kodeish. In a similar vein, Hashem is described as Kadosh because He is totally set apart from all of humanity. We are therefore commanded, "And you shall be holy (kedoshim) because I am Holy (Kadosh). Just as Hashem is completely set apart, so too, Bnei Yisroel should set themselves apart from the rest of mankind and be absolutely dedicated to Hashem.
How does one reach this level of kedusha? It can be reached through bitachon. He who has absolute faith in Hashem relies on Him entirely, and does not place his trust in any human being. Bnei Yisroel, with their bitachon, followed Hashem blindly into the wilderness and showed that they were devoted totally to Him. This complete devotion raised them to the level of kedoshim.