What does Turbotax mean by "This account did not have income, deductions, or credits associated with it in [year]"?

The question is asking: in your Form 1040, was there no income (interest, dividends, royalties, other income, gains), deductions, or credits that specifically pertain to this foreign financial account?

For example, for your foreign investment account that made $500 in dividends last year, you would have reported this interest as income on Line 2b Taxable Interest of Form 1040. You would then leave this box unchecked. For your foreign bank account that made $0 in interest, you would check this box.

More details: this screen in TurboTax is helping you fill out Form 8938, Statement of Foreign Financial Assets. Part III of this form asks you to aggregate all the income, deductions, and credits that pertain to all the foreign financial assets you're declaring on this form. Part V of the form asks you to provide further details on each foreign financial account. One of the lines in Part V is the checkbox you highlighted, Box 3d, which is labelled "No tax item reported in Part III with respect to this asset".