Does "deductions related to your foreign earned income" mean things that were deducted when I paid taxes on my income in the foreign country in which I earned it?

No, the deductions related to your foreign earned income are deductions on your return that relate to your foreign earnings.  Business expenses are an example.  If you have deducted business expenses on your return and some relate to your foreign earnings, then you would need to list the portion of business expenses that relate to your foreign earnings.

Deductions to foreign earned income can include moving expenses, other business expenses, or the employer-equivalent portion of self-employment tax paid on self-employed earnings in a foreign country.

These rules apply only to items definitely related to the excluded earned income and they do not apply to the other items that are not definitely related to an particular type of gross income. These rules do not apply to items such as:
- Personal exemptions
- Qualified retirement contributions
- Alimony payments
- Charitable contributions
- Medical expenses
- Mortgage interest
- Real estate taxes on your personal residence

If you are going to deduct these expenses or other expenses you will need to make sure you allocate the portion of expenses that are related to the foreign earned income you earned.