"e." is required because "e" is the table alias for "emp" table. Same thing for "d." - it is required because "d" is the table alias for "dept" table.
=> "e.deptno" means the "deptno column of the table whose alias is e i.e. emp table"
=> "d.deptno" means the "deptno column of the table whose alias is d i.e. dept table"

You can simply read out the query as regular text:

Code:

select <column_list>           -- select a list of columns
  from emp e, dept d           -- from the "emp" and "dept" tables
 where e.deptno = d.deptno;    -- where the "deptno" column of "emp" table equals the "deptno" column of "dept" table

=> The table alias is a shorthand for the table name. Instead of using the table name everywhere, I could use the table alias to keep the query short.
=> I did not have to use "e" and "d"; any alias would've been fine. The following query runs successfully.

Code:

select count(*) from emp x, dept y where x.deptno = y.deptno;

But it's a good practice to use a table alias that resembles or is a mnemonic for the table name.
A table alias is optional if all the tables are distinct. Without it, my query would've looked like this:

Code:

select count(*) from emp, dept where emp.deptno = dept.deptno;

However, if I use the same table more than once in the FROM clause i.e. if I join a table with itself, then the table alias is mandatory for the join. For example, in the following query, aliases are required (they do not have to be "e" and "m" though):

Code:

scott@PDBORA12C>
scott@PDBORA12C> -- List employees and their managers
scott@PDBORA12C> select e.ename as employee, m.ename as manager
  2    from emp e, emp m
  3   where e.mgr = m.empno;

EMPLOYEE   MANAGER
---------- ----------
FORD       JONES
SCOTT      JONES
TURNER     BLAKE
ALLEN      BLAKE
WARD       BLAKE
JAMES      BLAKE
MARTIN     BLAKE
MILLER     CLARK
ADAMS      SCOTT
BLAKE      KING
JONES      KING
CLARK      KING
SMITH      FORD

13 rows selected.

scott@PDBORA12C>

I must mention that there is other (ANSI specific) query syntax where the table alias could be avoided e.g. with the "USING" clause or the "NATURAL JOIN" clause.