The Hebrews came to Egypt after the story of Joseph (the guy with the technicolor dream coat). Joseph was down with the Egyptians and he invited his family to come over and live in this nice place with fertile soil and cool architecture and all that good stuff.
Somewhere along the line, though, things got ugly, and a pharaoh decided to make the Jews into slaves (boo!). So they got all enslaved and it was pretty sad.
Anyway, a pretty nasty pharaoh...I don't remember if it was the same one...well, anyway, a really nasty pharaoh got worried that these Hebrew dudes were going to multiply and outnumber the Egyptians and have too much power and take over the country. His solution was to take all the babies and toss them into the river to drown or get eaten by a hippopotamus (the hippopotamus's name was Joe-Bob Hippo III, but that's not important to the story).
One of the Hebrew ladies decided to get all clever, so she dumped her baby in the river like everyone else, but she put him in a basket first so that he would float and not drown, and she made sure Joe-Bob Hippo III wasn't looking. This is still pretty dangerous, and you should not put a baby in a river even if you are certain the basket is watertight, but I suppose it's still better than just drowning outright...I guess.
Well, in this case it worked out pretty well, because the baby got lucky and drifted safely over to the palace, where he was adopted and raised and named Moses, which is Egyptian for "Moses".
So Moses grew up thinking he was all Egyptian and whatnot, until at some point he got in trouble for killing some guy, I don't remember the exact reasons but he had to flee the country and run out to the desert. So he met up with some nomadic Jews and joined up with them and married some girl and ended up becoming a shepherd, and all in all Moses was pretty comfortable in his new life.
Then one day he was looking for a lost sheep when he saw a burning bush. It was a really weird burning bush because the fire burned but the bush wasn't consumed, and it gave all of his creatures haste which isn't something a normal bush does. Turns out the burning bush was God! Woah!
So God spoke to Moses and said, "Hey Moses, did you know you were adopted? You're actually a Hebrew." And Moses was like O_O. And then God said, "So I'm God and I want you to be my prophet. I need you to go to the pharaoh and tell him to let my people go." And Moses was all like >_>.
And so Moses told God, "God, I'd really love to do that, but I have this stutter and I'm t-t-terrified of public speaking." And God said, "Well, okay, since you have a speech impediment we'll get your brother Aaron to do the talking. Oh, yeah, I forgot to mention you have a brother. We'll have to get you guys together sometime."
So Moses went back to Egypt and he met up with his biological family and then they went to the palace to ask the pharaoh to release all the slaves pretty please.
They asked the pharaoh to release all the slaves, pretty please with a cherry on top, we'll be your best friend forever. The pharaoh said no. So Moses, to prove that God is awesome, took his staff and turned it into a snake! But the pharaoh's priests said, "Pff, is that all you got? Any two-bit deity can do that." And they did the same thing. The Jewish snake was way more badass than the Egyptian snakes, though, and they fought and the Jewish snake ate all the other snakes! Pharaoh, however, did not want to free a bunch of perfectly good slaves just because some dude had a badass snake, and told Moses and Aaron to take their God and shove it up their bums.
So God said to Moses, "Oh, is that how Pharaoh wants to play it? Well screw him, I'm going to send ten plagues down to Egypt and see how he likes that. And I'll harden his heart too, so that he'll take it and he'll damn well like it, bitch!"
And so God sent some pretty nasty plagues down to Egypt. First he turned all the water into blood. That didn't work because pharaoh's heart was hardened and anyway, what's a little blood? It improves the flavor!
Next, God sent a plague of frogs. Pharaoh's heart was hardened and anyway, there's good eating on those frogs.
Then God sent lice. Pharaoh laughed, ordered his servants to make him a new backscratcher, and turned Moses down once again.
For the fourth plague, God sent flies. Pharaoh's heart was still hardened, and the sales of backscratchers, flea powder, frog's legs, and flyswatters was causing a boom in the Egyptian economy. He rejected Moses once again.
For the fifth plague, God sent a pestilence to kill all the livestock. Pharaoh told Moses once again that he could stick his pestilence up his bum. (Joe-Bob Hippo III caught the pestilence too, and he ended up going on a quest to the magical land of the faeries to find a cure, but this story is not about Joe-Bob Hippo III.)
Then God gave all the Egyptians boils. Really bad boils, big oozy ones all over their bodies. And hemorrhoids. Gigantic hemorrhoids. Pharaoh was having a little trouble sitting down, but he still told Moses to piss off.
For the seventh plague, God made it hail. Really bad hail. Hailstones the size of dinner plates. By this point the Egyptians were starting to put political pressure on Pharaoh to deal with this stupid weather crap, but God hardened Pharaoh's heart and even as his approval rates dived, he refused to free the slaves.
The plagues continued with locusts. Big hungry locusts that ate all the crops and were too nasty to take out with the flyswatters from the fourth plague. But pharaoh was stubborn and, y'know, the wholw thing with the hardened heart, so he held his ground.
The ninth plague was darkness. God blotted out the sun. But this only caused the torch and candle industries to rack up incredible profits, and Pharaoh once again refused to relent.
Finally, Moses came to the pharaoh with a final ultimatum: let my people go, or all of the firstborn children of Egypt will die. Like actual dead. Pharaoh's heart was hardened, and even though he really should have listened, he refused.
Moses and Aaron told all the Israelites to sacrifice a lamb and to paint their doors with its blood, so that when death came to their household, it would see the mark and pass over harmlessly. The next morning, thousands of Egyptian children were dead, and the Hebrew children had been spared.
This was too much for pharaoh even with his hardened heart, and when Moses came to him again, he told Moses to take his people and leave the country and never come back, assholes.
So the Hebrews rushed out of their homes, taking with them only what they could carry or what they could grab from a storefront on the sly on their way out. They were in such a hurry that they had to take their bread from the oven before it could rise--this unleavened bread is now called matzo, and it has become a tradition to eat only unleavened bread during Pesach.
As they fled towards the Red Sea, Pharaoh had a change of heart and decided that it would be pretty bad for the economy to lose such a huge portion of the laboring class. So he sent the whole Egyptian army out to follow them and take them back by force. Meanwhile, Moses and his followers had reached the Red Sea, but had no way to cross, so Moses raised his staff and God parted the waters so that they could walk across the seabed to the other side.
But the Egyptians were catching up with them! They followed the same way. And so when all the Hebrews were safely on the opposite shore, Moses raised his staff again and the waters flowed back to normal, drowning the Egyptian army. Bam! Take that!
And so the Hebrew people escaped from slavery in Egypt. They would go on to wander in the desert for 40 years, where Moses would present them with the Ten Commandments, before eventually reaching the Promised Land of Milk and Honey and, y'know, all that stuff. And that's how Passover was made.