What would I use a MATCH SIMPLE foreign key for? What I understand:

In addition to valid references to the referenced table, a column with a foreign key is also allowed to hold a NULL value. The SQL standard defines several match modes for foreign keys, like MATCH SIMPLE and MATCH FULL. For multi-column foreign keys, MATCH SIMPLE allows a wrong (= not referencing) value in any of the columns as long as at least one column of the foreign key holds a NULL value.

Multi-column foreign keys are rare (because multi-column primary keys are), but I can imagine valid use cases. For example a translation of a blog post might have a primary key (post_id, language_id). Now something that references such a translation (for example which translation a user is currently editing) would have a multi-column foreign key.

What I don't understand:

Why would I ever use MATCH SIMPLE for my foreign key?

In above example it doesn't make sense to have a "currently editing" entry that only references by post_id and not by language_id.

What would be an example where it does make sense?
My preference is to avoid nulls in foreign key columns. Make all foreign keys non-nullable. In fact I have foreign key = not null as a standard check in some static analysis scripts I use for validating database designs.

The FULL / SIMPLE behaviour is obscure enough that in my experience even experts don't always get it (I'm an expert and I have to think twice about it!) As ypercube points out, SIMPLE is effectively the default in Microsoft SQL Server but I suspect most people working with that product never even considered it. If one of your goals in database design is to make data comprehensible by and useful to the average user then foreign keys ought to be non-nullable.