mysql replication successful but slave not replicating
The output you presented is very confusing. On one hand, the master shows:

mysql-bin.000001   639495 


The slave's PROCESSLIST indicates that replication works (the IO thread is connected to the master, the SQL thread is waiting).

The slave's SHOW SLAVE STATUS again claims all is well, but the master's position is 106.

Are all these outputs issued at roughly the same time? If not, then they are not valuable.

I would check the following:


The obvious: is 109.123.100.58 really your master?
Does SHOW PROCESSLIST on master list the connection made by the slave under the replica user?
Do you have different server-id settings for master and slave?
Do you have any replicate-do-* or replicate-ignore-* settings in your mysql.cnf file?