ACF stores data for custom field related to posts in the post_meta table, just like standard wp custom fields. It stores custom fields for everything else in the options table.
Every field has two database rows associated with it. The first is your standard meta_key => meta_value. The other is a reference entry, the meta_key is your field name with an _ (underscore) at the beginning and the value is the ACF field key. this tells ACF how to handle your value. The same pattern is used for options but the field names have more things added to the field names.
Some fields are far more complicated, like repeaters and flexible content.
All of the data stored using ACF can be retrieved using the standard WP function like get_post_meta and get_option if you use the right meta_key or option_name.
