Why did Julius Caesar travel to Egypt?
Because he was having an affair with Cleopatra
(Side note: Do you not think this should be in the History section?)
Julius Caesar was in love with the Egyptian queen Cleopatra, and they even had a son called Caesarion (who was executed by Augustus, supposedly). Therefore, Caesar would go to Egypt in order to check up on them.
It all began due to Caesar chasing Pompey after defeating him at Pharsalus (https://en.wikipedia.org/wiki/Battle_of_Pharsalus). Pompey thought it'd be a great idea to run off to Egypt, but he was killed as he arrived in Alexandria (by his Centurion). Caesar chased after him, and once he got there he was delivered Pompey's head by said Centurion.
Basically, Caesar then decided to get involved in the Egyptian civil war between the kid pharaoh, and Cleopatra (why he did so I have no clue, but it is speculated that due to the kid having to do something with Pompey's death). After defeating the pharaoh's armies at the Battle of the Nile (https://en.wikipedia.org/wiki/Battle_of_the_Nile_(47_BC)), he installed Cleopatra as ruler, and then proceeded to become infatuated by her.