If you are in a direct relationship with American Express (for example you've signed an Amex Card Acceptance Agreement) they may decide at some point to impose a Reserve, withholding some portion of the funds due from your transactions processed with Stripe.
If this happens, Stripe won't receive all of your expected funds. Instead, this portion of funds will appear under Held back by American Express in the Balances tab of your Stripe Dashboard. Once Amex releases their reserve, these funds will switch to available balance, subject to your usual payout schedule.
Amex typically notify users directly (not via Stripe) if they decide to impose or release a Reserve.
Unfortunately, Stripe is not told why Amex chooses to take this action, what their target reserved amount is, or for how long they intend to maintain it. This information can only be discussed with your American Express representative.