All that exists has a soul; everything from a rock to a blade of grass, to sheep grazing in a meadow(See source 1). Still, there are different kinds of souls, as the soul of a human is different from the soul of a tree. So too, the soul of a Jew is different than other types of souls.
The soul of a Jew is called a neshama. Torah calls a neshama “an actual part of G-d”, to indicate that it comes from G-d’s inner being(See source 2). Specifically, it comes from G-d’s thought and wisdom, a level called the Chochmah of Atzilus.
For background, we will define Atzilus and Chochmah. There are four spiritual worlds commonly discussed within the mystical part of the Torah. The most lofty of these four is called Atzilus, literally “emanation”, because it is an emanation of G-d/G-dliness. This world is the source of Jewish souls.
Chochmah is the attribute of cognitive inquiry. One uses this attribute when they inquire into a matter, or are open to it. Regarding Chochmah of Atzilus in particular, it is so lofty that it is called Higher Chochmah. It is also completely united with G-d, as Maimonedes states, “He and His Chochmah are one.” Thus, a neshama is one with G-d at a level that is near categorically beyond anything in our day to day experience.
There is almost nothing in the universe loftier than a neshama, a Jewish soul. This ought to give a Jew joy. The Rebbe once asked a Jew how he could not rejoice, knowing that his soul is “an actual part of G-d above”. Indeed, at one’s core he/she is a legitimate part of G-d, the most kind, just, and powerful Being in the entire universe. Nothing better than that!
Sources
https://www.chabad.org/library/article_cdo/aid/3194/jewish/What-is-a-Soul-Neshamah.html