"what I mean by that" is a perfectly correct and usable expression in written English. You can use it when you want to emphasize something you have just said, or to refer to a point that you have made earlier in the conversation. For example: "I think the government should invest more money in education. What I mean by that is that every child should have the opportunity to get a quality education, regardless of their background or financial situation."
Let me explain what I mean by that.
I think you know what I mean by that.
And let me explain what I mean by that.
Well, I've come to–I'll have to tell you what I mean by that.
You, you aristocrat, Won't know exactly what I mean by that.
I agree, and have been trying to pin down what I mean by that.
When I think of "America", it's usually difficult to disentangle exactly what I mean by that.
Here's what I mean by that.
All parents reading this know what I mean by that.
And what I mean by that is that she sounds like nobody else".
What I mean by that is the very concept of Palin is sexist.
Being a terminologist, I care about word choice. Ludwig simply helps me pick the best words for any translation. Five stars!
Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union