What does that mean? Does it mean that all people are identical? That if you attempt to measure people on some kind of scale the results will show that they are equivalent to each other? That no person is stronger or smarter or faster than any other? No, that would be obvious nonsense.
What it means is that people should be treated equally. That the law that applies to one person should apply to another equally. No one person should be privileged over another, but that they should be equal in both the rights assigned to them and the duties expected of them.
Society beyond a certain size needs rules - in small social groups it's possible to get by with ad-hoc decisions and informal methods for dealing with problems, but once you have social networks that are too large for each member to know every other member then rules are needed to ensure that all members of the group know what behaviour is (un)acceptable.
But why should we agree to treat all people equally? Why not bias the rules towards white people, male people, smart people or creative people? The basic reason is this - if you want people to follow a set of rules then either you need to get them to agree that those are the best set of rules or you need to enforce those rules against their will. Enforcing rules requires an infrastructure in and of itself, and the more people don't buy in to the rules the more enforcement is necessary. If the rules are generally considered to be unreasonable then there will either be mass disobedience or a police state.
The only way to mass agreement on the rules is to have rules that are agreed on by nearly all of the people. Some rules are simple enough that most people can agree with them without needing to invest a large amount of time in understanding them. "No Killing People" is simple enough to be generally considered acceptable, for instance, whereas international treaties on agricultural trade so massively exceed most people's interest levels that no more than a fraction of a percent of the population would take an interest. In addition there are many choices that will be sharply divisive, with no single answer being acceptable to all parties.
The answer to this problem is to have a method of producing rules that all people can agree to. Once the method is agreed on, everyone agrees that rules produced by it will be followed, allowing society to function and rules to be created without unanimity. Nobody likes to be left out of decision making agreement, but as mentioned above most people have no interest in the complex details of most rules (the fact that the rules for anything approximating real life need to be complex is another story, for another time), which inexorably leads to the idea of representative democracy, where the mass of people each vote for a person to uphold their interests, agreeing that the laws that these people produce will be followed.
It's not a perfect system (such a thing being, by definition, impossible), but it's the only one that has even a small chance of working in the long term. Anything else leads to feelings of dissociation from the rules that are produced, meaning that people will be less willing to follow them.
Of course, there are a fair number of different approaches to representative democracy, ranging from the traditional "first past the post" to "proportional representation" via numerous other different ways of interpreting and combining individual votes. Another topic for another time.