Around 3300 BCE, Egypt was split into two pieces: Lower Egypt in the north and Upper Egypt in the south. (Confused? The Egyptians were based on the Nile River, which started in the south. So they thought, "The Nile starts in our Upper land!" This was actually the south.)
Sometime between 3273 and 2987 BCE, call it c. 3100 BCE, the king, or pharoah, of Upper Egypt was Narmer. He conquered Lower Egypt and was able to wear the double crown, which was red and white combined into one crown. This signified the rule over both the white Upper Egyptians and red Lower Egyptians.
Following Lower Egypt, Narmer took over Canaan (Israel). Canaan had faced an attack from Lower Egypt, but had survived it. Now its tribes were subjugated, and Narmer had a huge empire.
After him, the dynasty he had founded (The First dynasty of Egypt) lasted for 200 more years, until around 2916 BCE, when the Second dynasty of Egypt appeared. The next few dynasties reigned for, on average, 150 years, until 2181 BCE, the end of the Sixth Dynasty.
The Great Pyramids of Egypt and the Sphinx were created in these dynasties' time.
After the Sixth Dynasty of Egypt, the empire broke into many kingdoms, causing the First Intermediate Period, which lasted until 2040 BCE. The First Intermediate Period was a time of quarreling between small kingdoms, each struggling to control Egypt (3 times during the Intermediate Period a dynasty took over Egypt), when the Seventh Dynasty took control of the country, and Egypt was at peace once more.