Before that gets you too excited or sceptical, let me say that end users will not really see many significant speed boosts. When I say end users, I mean people who are just loading packages and writing scripts where they plug variables into functions from the package. The reason these end users won't see much difference is that a well made Python or R package (including things like Numpy) are actually Python and R wrappers around C, C++, Fortran or Julia code. However, if you are trying to do something that your packages weren't directly designed to do and writing non-trivial code, then you're going to start seeing the speed advantages of Julia.
With all that in mind, I'd say the main reason for end users to use Julia is not the speed, it's the expressiveness and the top notch libraries.
Expressiveness is kinda a vague concept, but what I'm basically saying is that through things like multiple dispatch and macros, julia is able to provide ways of writing programs in almost any domain that feel incredibly natural and various programs will compose with eachother in ways you won't see in any language except Common Lisp.
Finally, because of Julia's native speed and expressiveness, it doesn't get in package developers way like Python and R do and so we're seeing that even though julia has a much smaller community than Python or R, we have a package ecosystem that's quite comparable and in certain specific regions, flat out superior. As adoption grows, we're going to see the julia package ecosystem accelerate and Julia will make sense for more end users.
For now, whether or not Julia makes sense for you really depends on what field you're working in (ie. if there are good packages already for the tasks you're interested in) and how advanced a programmer you are / want to be (ie. if you're going to be trying to do something that's not already covered by existing packages).