"regclass" is an alias for an Object Identifier, which are used internally by PostgreSQL as primary keys for several data dictionary tables.
It can be used as a translator when querying the dictionary tables in postgres. 
For example, the following query produces an error, since the predicate expects an integer ("oid"):
select relname,relowner,reltuples,relkind  from pg_class where oid='myuser.mytable_1';
ERROR:  invalid input syntax for type oid: "myuser.mytable_1"
LINE 1: ...lowner,reltuples,relkind  from pg_class where oid='myuser.mytabl...
However, if you add "::regclass", the alias for the object is used instead of the literal string:
 select relname,relowner,reltuples,relkind  from pg_class where oid='myuser.mytable_1'::regclass;
  relname  | relowner | reltuples | relkind
-----------+----------+-----------+---------
 mytable_1 |    69094 |         0 | p
Note that there are several types of OIDs. For example, for roles (users), you should use "regrole" instead of "regclass":
select relname,relowner,reltuples,relkind  from pg_class where relowner='myuser'::regrole;
        relname        | relowner | reltuples | relkind
-----------------------+----------+-----------+---------
 unique_idx_2          |    69094 |         0 | I
 pg_toast_191274       |    69094 |         0 | t
 mytable_1_id_seq      |    69094 |         1 | S
 mytable_1_pkey        |    69094 |         0 | I
 unique_idx_1          |    69094 |         0 | i
 mytable_2             |    69094 |         0 | p
 mytable_3             |    69094 |         0 | r
 
If you use them together, translate to different types of OID. In the below case, it's really not necessary, but illustrates the point nevertheless:
 select relname,relowner,reltuples,relkind  from pg_class where oid='myuser.mytable_1'::regclass and relowner='myuser'::regrole;
More information about 
OIDs
More information about 
pg_class