From phpBB Development Wiki
Beginning with phpBB 3.1, database updating is performed using Migrations.
Migrations was built because of the difficulties of distributed development and maintaining an updated database setup across all developers.
RFC Topic if you're interested in the reasons: http://area51.phpbb.com/phpBB/viewtopic.php?t=41337
What does Migrations mean for me?
As a user
Migrations does not affect using phpBB, only writing code for it, so Administrators do not have to do anything differently.
Database updates between versions of phpBB and Mod/Extension updates will be safer and, in the unlikely event something happens during database changes, much easier to debug and correct.
Functionality similar to UMIL built into phpBB (easier management of database changes between versions, helpful tools to assist making database changes).
As a Developer
Easier collaboration with others, less time spent managing database changes between different branches and pull requests.
How do I use Migrations?
Getting started with Migrations
How to create a basic Migration file
How to use Migration helpers to perform basic database changes
Using Migrations in an Extension
How to use Migrations in your Extension to make database changes