Turning on international time/date formatting
Date formatting is changed per-language. For instance, English (US) and Français (Canada) will see a MM/DD/YYYY format.
If you want to view Trello in English, but use international date formatting, you can change your language to English (UK) from English (US).
To change your language, click your name in the top right, then "Change Language..." (if you're using an Atlassian account, the language will have to be changed from your Atlassian account preferences instead on https://id.atlassian.com/manage-profile/account-preferences)
This will cause Trello to show Monday as the first day of the week, show dates as DD/MM/YYYY, and use 24-hour time.