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The column aliases there override the column names/aliases of the internal select subquery (derived table). The same way, they can override the column names of the table (whether it's base table, a view, a derived table or a cte does not matter at all).

So, in the simple example:

select 
    b, count_b            -- valid column aliases
    a, count_a            -- invalid here (have been overridden)
from 
    ( select t.a, count(*) as count_a
      from t
      group by t.a
      order by count_a desc           -- count_a is valid here
      limit 8
    ) 
      as d (b, count_b) ;

the names a and count_a are valid inside the subquery (derived table) but not outside because they have been overridden by b and count_b.

Do you have to know the exact sequence of columns defined in the table, or can you set an alias just for one or two of these in the FROM clause?

Yes, you do have to know the sequence of columns.

But you don't have to change all columns. Say the table has 5 columns. If you use:

select t.*
from table_name as t (a,b,c) ; 

only the first 3 columns will appear with the new names (a,b,c). The 4th and 5th will show with their real names. You'll get an error if you provide more aliases than needed (eg. 6 aliases for a 5-column table).

What if you only want to set a column_alias for one column with a very long name (and leave the other columns not aliased); is this possible? (If so, is this Postgres specific?)

Only if it's the first. Or by providing all the previous column names up to the column you want to alias with a different name.

I suppose you can't just give an alias for the third column only, or something like that?

I don't know of any syntax to allow you to alias only the 3rd column, without providing the names of the 1st and 2nd column.

Overall, the usefulness of the feature is at least debatable when used for base tables. And the above query that overrides the names of just 3 of the possibly many columns reeks obfuscation and could be very well considered bad practice.

But the feature is provided because it's standard SQL and for completeness. It wouldn't make sense to have this only for subqueries and CTEs and not for other kinds of tables.

One case where it can be useful is (not with base table but with) the VALUES construct, where the columns get default names of column1, column2, etc. and this aliasing can be used to select more meaningful names:

select 
    a, b
from 
    ( values
         (1, 2),
         (2, 3), 
         (3, 5)
    ) 
      as d (a, b) ;