This kind of query is called a correlated sub query. For your requirement, the query would be as below....
update students s
  set s.department = (
          select e.qualification
            from employee e
            where s.uniquename = e.uniquename 
              and s.Homecountry = e.Homecountry
       );
updating this post based on your replies below.
Again, going forward, always post the create table and insert statements (and the expected results) to reproduce your case. If you don't see the expected results or if you see an erro when you execute the query, post the exact message instead of just saying "not working". Here is the results of my sqlplus session. 
---create table and insert statements
create table student(
     name varchar2(20),
     age  number,
     department varchar2(3),
     HomeCountry varchar2(10)
    );
Table created.
create table employee5(
     name varchar2(20),
     exp  number,
     qualification varchar2(3),
     homecountry varchar2(10)
   );
Table created.
insert into student values ('Mohan',25,'EEE','India');
insert into student values ('Raja',27,'EEE','India');
insert into student values ('Ahamed',26,'ECE','UK');
insert into student values ('Gokul',25,'IT','USA');
commit;
insert into employee5 values ('Mohan',25,'ECE','India');
insert into employee5 values ('Raja',24,'IT','India');
insert into employee5 values ('Palani',26,'ECE','USA');
insert into employee5 values ('Sathesh',29,'CSE','CANADA');
insert into employee5 values ('Ahamed',28,'ECE','UK');
insert into employee5 values ('Gokul',29,'EEE','USA');
commit;
Before updating the data...
SQL> select * from student;
NAME                        AGE DEP HOMECOUNTR
-------------------- ---------- --- ----------
Mohan                        25 EEE India
Raja                         27 EEE India
Ahamed                       26 ECE UK
Gokul                        25 IT  USA
SQL> select * from employee5;
NAME                        EXP QUA HOMECOUNTR
-------------------- ---------- --- ----------
Mohan                        25 ECE India
Raja                         24 IT  India
Palani                       26 ECE USA
Sathesh                      29 CSE CANADA
Ahamed                       28 ECE UK
Gokul                        29 EEE USA
Update statement and results
  1  update student s set s.age =
  2     ( select e.exp
  3          from employee5 e
  4          where e.name = s.name
  5            and e.homecountry = s.homecountry
  6*    )
SQL> /
4 rows updated.
SQL> select * from student;
NAME                        AGE DEP HOMECOUNTR
-------------------- ---------- --- ----------
Mohan                        25 EEE India
Raja                         24 EEE India
Ahamed                       28 ECE UK
Gokul                        29 IT  USA
SQL> commit;
Commit complete.