How to make user defined function descriptions ("docstrings") available to julia REPL?

You can use the @doc macro in Julia versions 0.4 (Oct. 2015) and above.

% julia
               _
   _       _ _(_)_     |  A fresh approach to technical computing
  (_)     | (_) (_)    |  Documentation: http://docs.julialang.org
   _ _   _| |_  __ _   |  Type "?help" for help.
  | | | | | | |/ _` |  |
  | | |_| | | | (_| |  |  Version 0.4.0 (2015-10-08 06:20 UTC)
 _/ |\__'_|_|_|\__'_|  |  Official http://julialang.org/ release
|__/                   |  x86_64-apple-darwin13.4.0

julia> @doc """
       Compute 2 times x minus y squared.
       """ ->
       function f(x::Float64, y::Float64)
           return 2x - y^2
       end
f (generic function with 1 method)

julia> @doc f
  Compute 2 times x minus y squared.

Edit: As pointed out by @Harrison Grodin, versions 0.5 and above support an abbreviated syntax as well as Markdown, LaTEX, and a few other goodies:

"""
Calculate the left Riemann sum[^1] approximating ``\int_a^b f(x) dx = F(b) - F(a).``

[^1]: Thomas G., Finney R. (1996), Calculus and Analytic Geometry, Addison Wesley, ISBN 0-201-53174-7
"""
function rs(a, b, d, f)
end

There are more details in the documentation.

In Julia v0.5+ (including more recent Julia Versions like 1.2+), you can write a multiline string above the function definition. (No need for @doc anymore.)

julia> """
           cube(x)

       Compute the cube of `x`, ``x^3``.

       # Examples
       ```jldoctest
       julia> cube(2)
       8
       ```
       """
       function cube(x)
           x^3
       end
cube

help?> cube
search: Cdouble isexecutable Ac_mul_B Ac_mul_Bc Ac_mul_B! Ac_mul_Bc! cumsum_kbn

  cube(x)

  Compute the cube of x, x^3.

     Examples
    ≡≡≡≡≡≡≡≡≡≡

  julia> cube(2)
  8

For more information on properly formatting your docstrings, see the official Julia Documentation.