On Server 1:

$> mysqldump --databases db1 > dump.sql

Copy the dump file from Server 1 to Server 2.

On Server 2:

$> mysql < dump.sql

Use of --databases with the mysqldump command line causes the dump file to include CREATE DATABASE and USE statements that create the database if it does exist and make it the default database for the reloaded data.

Alternatively, you can omit --databases from the mysqldump command. Then you need to create the database on Server 2 (if necessary) and to specify it as the default database when you reload the dump file.

On Server 1:

$> mysqldump db1 > dump.sql

On Server 2:

$> mysqladmin create db1
$> mysql db1 < dump.sql

You can specify a different database name in this case, so omitting --databases from the mysqldump command enables you to dump data from one database and load it into another.