The Eye of the Needle

Jerusalem was surrounded on all sides by walls for defense from numerous enemies, like a fort, with various gates for entry from outside, most narrow enough to provide an easy defense. The narrowest of all these gates was called "The Needle", due to its extremely narrow size and length. In order for camels to pass through he Needle gate (usually called "eye of the needle" for the parable, since "passing through a needle" would make no sense to us), they had to remove all baggage and everything from the camels, then they could get through the gate. Those caravans with heavy freight surely chose a wider gate for entrance, but hence the saying.

It's easier for a camel to give up its goods and continue passage to the Holy City, or Jerusalem, than for a rich man to enter the kingdom of heaven, which involves being willing to give up everything in the material world to enter. Most people think "give up worldly possessions", but it means leaving family behind too, also part of the material world - so it's most likely a reference to death. It's a spiritual quest, so you have to be willing to leave the material realm and your physical body.

The implication of mentioning a "rich man" is that the wealthy may be stronger bound to their possessions than someone poor, and less willing to leave the material world behind.