What does “analytically nuanced and capable of distinguishing different dimensions” mean?

“Analytically nuanced”

It means an argument does not treat a complicated historical phenomenon as if it had only one dimension.

For example, this is relatively simple:

Emancipation created equality.

A more nuanced argument distinguishes:

Emancipation created legal freedom, but legal freedom did not necessarily produce equal economic resources or equal social status.

Now you have separated three dimensions:

• legal — What does the law say?
• economic — Who owns land, capital, and productive resources?
• social — How does society actually regard and treat people?

Example

Suppose the law says:

A formerly enslaved Black man is legally free and has the same legal rights as a white man.

But society may still:

• regard him as inferior;
• refuse to accept him as a social equal;
• segregate him;
• deny him social recognition;
• use violence to enforce racial hierarchy.

So legal equality exists, while social equality remains incomplete.

That is what I mean by distinguishing different dimensions.