Here's what the MicroStation help file says about it:
Modified (Out-of-Synch asterisk) – identifies whether the level has been
modified. Displays if one or more of the working file level's attributes or
properties differ from the library source level. Properties are not
synchronized unless they are specified by MS_LEVEL_SYNC_ATTRIBUTE_LIST.

It also displays if the attachment level is also out-of-sync with it's
attachment source. Set
MS_LEVEL_DO_NOT_SYNCHRONIZE_ATTACHMENT_LEVELS_TO_DGNLIB in a configuration
file if you want to synchronize the attachment level with the attachment
source.

A tool tip listing the out-of-synch attribute or property displays when the
cursor is over the modified icon.

There is more than one way to do this.

The simplest way to attach a dgnlib to a single file is this:

1. Open the file that you want to attach the dgnlib to.

2. Load Level Manager (Settings | Level | Manager)

3. Choose Levels | Library | Attach…

4. Navigate to and select the dgnlib file.