Ditto Rafa. Let me add:
Having an index makes find a desired record faster. But it makes inserting and deleting records slower and it uses more disk space and other resources.
So it's a trade-off. If you will rarely or never use a certain field to find a record, there's no point creating and maintaining an index for it. Like suppose you had a database with customer names. Indexing on last name probably makes sense. You probably do a lot of searches by last name. But if you had a field for Junior/Senior/Esq/etc, there likely wouldn't be much point in indexing on that. How often would you say, "We don't know his account number, we don't know his name, we don't know his address, but we do know that he's a 'Junior'".
If a database is read very often but updated rarely, you might go ahead and create indexes in the close cases. If a database is mostly written and rarely read -- like a transaction archive maybe -- that would be a reason to have fewer indexes.