Hi Bijan,
This warning is triggered by having tables, in your database backup, which are marked as having the “utf8mb4” collation. That collation does not exist on MySQL 5.1 (and as such, can usually be used as a reliable proxy for the MySQL version of the source database). As such, if you have tables marked as having that collation (MySQL will allow PHP code to mark anything as the collation… but will silently corrupt data in the background if you use one that it doesn’t know about), then that’s potentially a serious problem. You should use phpMyAdmin on your source site, to go through your tables, and identify their collation… and, after taking a backup for safety, re-mark the utf8mb4 ones as utf8 , prior to testing the site (and particularly any features used by the identified tables), and then taking a fresh backup for migration.
David