How can I explain a word used in a previous sentence?

Your two examples are focusing on the word "that":

What "small" here means is, that, ...

What "small" here means is ...

You could use "that" but it shouldn't have the commas and I much prefer it without the "that".

But I think the bigger problem is the order of "here" and "means":

What "small" means here is...

You could also remove "what":

"Small", here, means...

Which gives us these final examples:

X is a small Y. What "small" means here is less than 30 inches.

X is a small Y. "Small", here, means less than 30 inches.

Other options:

X is a small Y. "Small" means less than 30 inches.

X is a small Y ("small" meaning less than 30 inches).

X is a small Y. "Small" in this context means "less than 30 inches."