To understand Serbs, you need to first know how they came to be.
Original Serbs were a Slavic tribe that settled in the Balkans during early middle ages. Their original territory covered roughly what is now eastern Herzegovina (east of Neretva river) and Montenegro. In 13th century, Serbs became the most powerful tribe in the region, under Nemanjić clan, descendants of Stefan Nemanja. At their peak, their territory spread south into Greece all the way to the Gulf of Corinth, included Sofia and Struma valleys that are now in Bulgaria, and had Bosnia as its vassal. Religiously, Serbs were firmly under Byzantine sphere of influence (unlike Bosnia) and Serbian Church was autocephalous since 1219, raised to a patriarchate in 1346.
What happened next is a disastrous defeat to Ottomans at Battle of Kosovo in 1389, which became the foundational myth of modern Serbia. Modern Serbs believe that because Serbia was too strong, Vatican and Ottomans joined in a conspiracy that to this very day is aimed at oppressing Serbs whenever possible. For example, Bill Clinton and The Hague War Tribunal are also part of this conspiracy.
What happened to Serbs after 1389? First, a century-long decay of Serbian state into oblivion. But Serbian Church retained its status, even under Ottomans, across the wide territory of medieval Serbia at its peak, and by the 19th century church membership became synonymous with Serbdom. Since not all ethnic groups had their own church, this also included now-Slavicised-previously-Romanised Illyrians ("Vlachs"), those Gypsies who became Christian, and even some ethnic Albanians (for example, Karađorđe Petrović, who became the leader of "First Serb Uprising" in 1804, his paternal grandfather was Đin Maraš Klimenta - Klimenti were an Albanian tribe, called Kelmendi in Albanian).
Meanwhile, in the original heartland of the Serbs, a resilient resistance against Ottoman rule was organised, now without a clear king, in 1516 in Cetinje. To avoid clan disputes, they agreed to name instead the Metropolitan of Zeta, now stationed in Cetinje, as their leaderhead. Ottomans found those remote mountain clans too much of a hassle to subdue and thus, de facto independent state of Montenegro was formed, which much later earned formal recognition.
tl;dr: Serbs are a "my ancestor))))))" hodgepodge of assorted trash mythologising a medieval identity that has barely anything to do with them. The only real Serbs are Montenegrins.