Adding my 2 cents:
Python was not relatively new in the early 00's, but its popularity really started taking off around that time. It is older than Java and Javascript.
Ruby became big primarily because of Ruby on Rails. Python was already big before Django came around. In fact, one of the reasons Django exists is "Python is cool, and we need a good web framework for it".
Why was it already popular? My guesses:
Very easy for new programmers, but enabled you to build fairly powerful stuff with it (unlike, say, BASIC). Eric Raymond, around 2000, wrote an article on why he loved Python, and the main takeaway was that within a day or two of encountering it, he was already building useful scripts with it.
It is fairly well designed (well, at this point it may be overdesigned). A common remark by people learning Python was "I didn't know how to do X, so I guessed and it worked!"
Has some functional programming aspects that appealed to people (e.g. lambdas, map, reduce, filter, etc). Has laziness if needed.
But the real reason: It was not Perl, and was a viable alternative to it. It explicitly was against Perl's philosophy of "There's more than one way to do it."
Batteries included: Every standard Python distribution came with what was then a really good set of libraries. Sure, Perl had CPAN which was more extensive, but consider that not everyone had high speed Internet, and you still have to do the labor of identifying which CPAN package you wanted. For many Python developers, the standard library was all they needed.
Then with NumPy, it became a good alternative to MATLAB. Although started to be heavily used in scientific computation 2006 onwards. With pandas people started abandoning R for it, even though R is, and continues to be, a better statistics language. With Numpy and Pandas available, machine learning easily followed in the early 2010s.
The benefit of Python over stuff like R and MATLAB (and possibly JS) is that you have access to all the other libraries. In those days, if I wanted to write some code in MATLAB, but have it also crawl some web pages, and do some scripting, it was a pain. You'd write the MATLAB code to deal with the computation, and separate scripts for the rest. Now I can do it all in one language/program.
And yes, I'll say it: Whitespace. The lack of braces and semicolons, and the semi-rigidity of whitespace just made it a lot easier to read.