What is the meaning of this?
In random projection, the original d-dimensional data is projected to a k-dimensional (k << d) subspace through the origin, using a random k × d matrix R whose columns have unit lengths.
I have already searched around the internet and can't find a straight answer. Does it mean that each column sum of values is equal to one?
Columns have unit length, typically means, the following:
If $a_i$ is the $i^{th}$ column in a matrix, then $\Vert a_i \Vert_2 = 1$, where $\Vert \cdot \Vert_2$ is the two-norm of a vector.
So for instance, the matrix below has columns of unit length:
$$A = \begin{bmatrix}1/2 & \dfrac1{\sqrt2}\\ -\dfrac12 & 0\\ -\dfrac1{\sqrt2} & \dfrac1{\sqrt2}\end{bmatrix}$$ since $$\sqrt{\left(\dfrac12\right)^2 + \left(-\dfrac12\right)^2 + \left(-\dfrac1{\sqrt2}\right)^2} = \sqrt{\dfrac14 + \dfrac14 + \dfrac12} = 1$$ $$\sqrt{\left(\dfrac1{\sqrt2}\right)^2 + 0^2 + \left(\dfrac1{\sqrt2}\right)^2} = \sqrt{\dfrac12 + 0 + \dfrac12} = 1$$