insert into yourTableName2(yourColumnName1,...N) select yourColumnName1,..N from yourTableName1;

mysql> create table DemoTable1(FirstName varchar(100));
Query OK, 0 rows affected (1.11 sec)

mysql> insert into DemoTable1 values('John');
Query OK, 1 row affected (0.31 sec)
mysql> insert into DemoTable1 values('Chris');
Query OK, 1 row affected (0.13 sec)
mysql> insert into DemoTable1 values('Bob');
Query OK, 1 row affected (0.40 sec)

mysql> select *from DemoTable1;

+-----------+
| FirstName |
+-----------+
| John      |
| Chris     |
| Bob       |
+-----------+
3 rows in set (0.00 sec)

mysql> create table DemoTable2 (EmployeeName varchar(100));
Query OK, 0 rows affected (0.78 sec)

mysql> insert into DemoTable2(EmployeeName) select FirstName from DemoTable1;
Query OK, 3 rows affected (0.52 sec)
Records: 3 Duplicates: 0 Warnings: 0

mysql> select *from DemoTable2;

+--------------+
| EmployeeName |
+--------------+
| John         |
| Chris        |
| Bob          |
+--------------+
3 rows in set (0.00 sec)