When users reach trust levels 2 and 3 they are awarded a badge and will receive a notification for the badge. For Trust Level 2, users are granted the Member badge. For Trust Level 3, they are granted the Regular badge. The notificaitons for these badges link to a description of the user’s new capabilities.
The badge descriptions can be edited through your Admin / Customize / Text Content section.
There is a discussion about sending PMs for trust level 2 and 3 promotions here: Send Promotion PMs.