Learn Swedish: Släktforskningen handlar om hembygden, om vars historia jag hade läst. - The genealogy is about the native district, about whose history I had read.

The first om belongs to handlar om (is about). The second om belongs to the relative clause. The verb läsa takes the preposition om (to read about). In this formal structure, the preposition is moved to the very front of the relative clause, giving us om vars historia (about whose history).

How would this relative clause look in everyday spoken Swedish?

In everyday speech, it is much more common to leave the preposition at the end of the clause. A Swede would typically say vars historia jag hade läst om instead of the highly formal om vars historia jag hade läst.

What does hembygden mean, and how is it different from a hometown?

Hembygd (here in the definite form, hembygden) means native district or home region. It refers to a broader geographical and cultural area than just a specific hometown (hemstad or hemort), and it carries a strong nostalgic connection to local history, nature, and roots.

Could I say släktforskningen är om instead of handlar om?

No, that would sound very unnatural in Swedish. When describing the subject, topic, or plot of something like research, an article, a book, or a film, you must use the phrasal verb handlar om.