Let's start by talking about love in human terms. Why does Person A love Person B? There can be a couple of possibilities:
It may be based on B's actions (for example, B has done something that A really appreciates).
It may be because of their relationship (a parent loves a child).
When we talk about G-d loving the Jewish people, both of these factors come into play.
He had a Torah, which we Jews accepted (and indeed, our tradition has it that He first "shopped around" the Torah to all of the other contemporary nations, who rejected it). This means, therefore, that we are the ones now tasked with the job of making the physical world into a home for spirituality - the purpose for which G-d created the universe in the first place.
(In Jewish tradition, all non-Jews are bound by the Seven Noahide Laws, including basics of civilization such as the prohibitions against murder and theft. G-d appreciates and rewards those who act accordingly - they are known as chassidei umos haolam, the righteous among the nations of the world, and have a share in Paradise. But that's not the same thing as transforming a physical object into a container for G-dliness, something which can be accomplished only through the positive commandments of the Torah.)
There is also the idea that a Jew has two souls, of which one is "literally a part of G-d above" (Tanya, ch. 2), so that there is somewhat the same relationship between G-d and a Jew as between a parent and child. Non-Jews have souls too, of course, but these are much like any other of G-d's creations - being that appear to be self-sustaining and independent of G-d.
One corollary of all of this, though, is that this doesn't necessarily mean that Jews enjoy preferential treatment. On the contrary, G-d has much higher expectations of Jews - meaning that our slipups are much more serious and carry greater consequences. "Only you have I known [intimately] among all of the families on earth," says the prophet in G-d's name, "therefore I will call you to account for all of your sins" (Amos 3:2). Or, as the popular expression has it, "With great power comes great responsibility."