The Imrei Emes zy’a (quoted in Sefer Likutei Yehuda) explains this pasuk by quoting the Magen Avrohom (46:10) who says in the name of Mekubalim that we make the brachos of ’shelo asani goy’ and ’shelo asani aved’ in the morning to thank Hashem for not allowing the neshamos of a gentile or a slave to enter our bodies while we slept. He asks: How does a person know that the nashama of a non-Jew did not enter his body? If he is able to bless Hashem and utter His name, it is a clear sign that this did not occur.
Accordingly, the pasuk is saying: ’And I will make a separation between My people and your people; this sign will come about tomorrow (in the morning)’ – every morning, when one recites Birchas Hashachar, the separation between a Jew and non-Jew is evident.
A Daily Transformation:
He states further that the reason the ’Yid Hakadosh’ was known by this name was because he sanctified himself every day to rise to a new level of holiness that was as far above his previous level as the difference between a Jew and a non-Jew. This concept is seen from this pasuk that says that the separation between a Jew and non-Jew is seen every morning, which means that a Jew is able to undergo a transformation every day in which he reaches a new level that is as far from his old level as the difference between a Jew and a non-Jew.