There were other men named Herod, including his son Herod Antipas (who killed John the Baptist), his grandson Herod Agrippa I, and his great-grandson Herod Agrippa II. Unfortunately, the New Testament uses the name "Herod" for more than one ruler, making it hard for many readers to know which person did what.
Fortunately, with the help of Josephus, we're able to sort out who the different New Testament rulers were, and why they were so important.
The Herod of Matthew 2, Matthew 14, and Acts 12 were in fact three different people.
His grandfather Antipas, about whom little is known, lived in Idumaea (biblical Edom). Judah Maccabee's nephew Hyrcanus I forcibly converted the inhabitants of Idumaea to Judaism in the 2nd century BC, inadvertently and indirectly paving the way for Jerusalem's destruction.
A generation later, Antipas's son Antipater aligned himself with Hyrcanus II, the Jewish leader who lost power when he disobeyed the mighty Roman leader Pompey. But when Julius Caesar took Pompey out of the picture, Antipater along with Hyrcanus II found a second opportunity to cozy up to the Roman power structure. Now aligned with Caesar, Hyrcanus II became Jerusalem's High Priest, and Antipater's children were put in charge of Jerusalem and the Galilee. His older son, Phasael, got Jerusalem. The Galilee went to his younger son, Herod.
Rome declined further into chaos with Caesar's assassination and Mark Antony's violent ascension to power. In the year 40 BC Rome lost Jerusalem to a group of people from the east called the Parthians. The Rome-aligned leader of Jerusalem, Phasael, is reported to have killed himself, opening up the position for Herod, who told Rome he would force the Parthians out.
It took Herod two tries, but in the year 37 he successfully recaptured Jerusalem.
This is how Herod, a Roman crony who was only technically Jewish by virtue of a forced conversion, came to rule the Jewish capital. He was so despised by the locals that he needed a Roman legion to guard him while he was in Jerusalem. But he had Rome's backing, so he could do whatever he liked.
Mostly what he did was build. He enlarged the Second Temple, built a fortress at Masada, and even built a town, called Herodium. He financed these massive works and his extravagant lifestyle by imposing burdensome taxes.
When he died in the year 4 BC, he left a population that was impoverished, alienated, and despondent. This was the Jerusalem into which Jesus was born.
Herod's son Herod Archelaus took over for a while, but due to his monumental ineptitude, Rome quickly replaced him.
Aristobulus IV, another of Herod the Great's sons, himself had a son by the name of Herod Agrippa I. This is the King Herod of Acts 12, who had John's brother James killed (Acts 12:2) before arresting Peter one verse later.