Learn Italian: Leggono il volantino prima della manifestazione. - They are reading the flyer before the demonstration.

When the word prima (before) is followed by a noun, it needs the preposition di to connect them. Here, di combines with the feminine definite article la (matching manifestazione) to form the combined word della.

Does manifestazione mean "manifestation" here?

It is a bit of a false friend! While it can translate to "manifestation" in a broad sense, in everyday Italian una manifestazione almost always refers to a public demonstration, rally, or protest.

Where does the word volantino come from?

It comes from the word volante (flying). A volantino is a flyer or leaflet—literally a little piece of paper that "flies" around as it gets distributed to a crowd.

Which syllable gets the stress in leggono?

The stress is on the first syllable: LÈG-go-no. In the present tense, the loro (they) form of many regular verbs drops the stress back to the root, which often trips up learners who want to stress the second-to-last syllable.