Joins return the rows from the first table linked to each row in the second where the join criteria are true.

1 = 1 is always true.

So this returns every row joined to every other row. aka a cross join:

create table t1 (
  c1 int
);
create table t2 (
  c1 int
);

insert into t1 values ( 1 );
insert into t1 values ( 2 );

insert into t2 values ( 1 );
insert into t2 values ( 2 );

select * 
from   t1
join   t2
on     ( 1 = 1 );

C1   C1   
   1    1 
   1    2 
   2    1 
   2    2

I can't think of a good reason for doing this*. If the intent is a cross join, then you should write that:

select * 
from   t1
cross join t2;

C1   C1   
   1    1 
   1    2 
   2    1 
   2    2 

* It's possible this is part of dynamic SQL. When constructing join and where clauses, it's handy to start with a base, always true condition. This make it easier to tack on extra predicates. Without having to sort out the where/on/and to start:

stmt := 'select * from t1 join t2 on 1=1 ';

if ... then
  stmt := stmt || ' and <some other test> ';
end if;

if ... then
  stmt := stmt || ' and <yet another test> ';
end if;

Though join criteria are usually fixed. So it's rare this is useful in your join clauses.