Hello!

There is no special tool yet which allows to export permissions(membership levels) data. So, you should save database tables to backup the data.

sys_acl_actions - contains the list of the all available membership levels' actions and from which modules they are.

sys_acl_actions_track - info about profiles and how many times they performed each of the membership action.

sys_acl_levels - list of the all existed membership levels 

sys_acl_levels_members - profiles with associated with them membership levels 

sys_acl_matrix - settings of each membership levels' action

bx_acl_level_prices - this table from Paid Levels (it is not default module). It contains paid info about each paid membership level.

If you like to save current state of the permissions (membership levels) with actions and profiles info, then you should save the all tables.

If you just need the list of the all membership levels without modules actions and members settings, then sys_acl_levels with bx_acl_level_prices (if you have the module) would be enough.

If you just need info about permissions and membership actions without profiles info, then sys_acl_actions, sys_acl_levels, sys_acl_matrix, bx_acl_level_prices (if you have paid module)