This happens because your Charset and collation are not utf8, utf8_general_ci.
You have a few options in order to fix this:
1) (recommended and simplest) Use phpMyAdmin to change your collation, this is a fairly simple task.
Depending on the version your using here's how for ver 3.4.5:
When logging into phpmyadmin on the left panel you will see your databases, select the one you used for wordpress. Then you will see all the tables in that same panel, select the table you would like to edit. Then you can click Operations on the top menu and in Table options change the collation.
2) You can set a new default for your entire database.
3) Recreate your table setting the default Charset and Collation here's how:
$sql = "CREATE TABLE $my_table_name (
id BIGINT(20) NOT NULL AUTO_INCREMENT,
message TEXT NOT NULL,
)DEFAULT CHARACTER SET utf8 COLLATE utf8_general_ci;";
require_once(ABSPATH . 'wp-admin/includes/upgrade.php');
I suggest if your creating a theme or plugin you set a default charset and collation for your table.