In the Dune universe, you have a few key groups:
1. The Emperor (head boss of the universe)
2. The Bene Gesserit (sneaky witches pulling the strings behind the scenes)
3. House Atreides (Paul & co)
4. The Harkonnens (the house opposing the Atreides, basically the Nazis dudes of the Dune story)
The planet Arrakis (aka Dune, a desert planet) produces the Spice drug, which is basically a brain steroid that could make you live three times as long. It turns your eyes blue & everyone in the universe is hooked on it. The Emperor assigns management of Arrakis to a House. The Atreides got to take over Dune because the Harkonnens were screwing up production & thus profits. But really, Hosue Atreides was getting pretty popular, so the Emperor wants to take them out. By giving them Dune, it casts a shadow on House Harkonnen, who then will want to take out House Atreides, meaning the Emperor can wipe out a political threat and get more control over the Harkonnens.
To compare it to modern politics, think of Dune like the Middle East & Spice like oil. Everyone needs it & everyone wants to control it. To simplify & put a stereotypical political spin on it, think of the Russians as House Harkonnen & America as House Atreides, then private companies with lobbyists as the Bene Gesserit, pulling the strings behind the scenes & lining things up to get the outcome they desire.
Meanwhile, the Bene Gesserit are kind of running the show behind the scenes. One of their projects is a long-term breeding program designed to produce the Kwisatz Haderach, which is basically their version of a Super Saiyan, who can use the spice to unlock all of the various benefits in a single person. The culmination of the bloodlines is for Duke Leto Atreides (Paul's dad) to have a daughter, who marries into House Harkonnen. Except Paul's mom goofs up 10,000 years of selective breeding by choosing to have a boy instead of a girl. Feyd could have married the female version of Paul & produced the Kwisatz Haderach.
So the Bene Gesserit need some way to save the bloodline, so they send someone to seduce Feyd in order to obtain a child that has his genetic material. Because he's so dangerous, their envoy also hypnotizes him using a special command word that can paralyze him. He almost kills Paul in one-on-one combat, but Paul refuses to use that keyword because he doesn't want to be beholden to the Bene Gesserit, so Paul has to use his own training to defeat Feyd. For the rest of the story, stayed tuned for the movie!