Other answers have given clear enough examples of a record referencing another record in the same table.
There are even valid use cases for a record referencing itself in the same table. For example, a point of sale system accepting many tenders may need to know which tender to use for change when the payment is not the exact value of the sale. For many tenders that's the same tender, for others that's domestic cash, for yet other tenders, no form of change is allowed.
All this can be pretty elegantly represented with a single tender attribute which is a foreign key referencing the primary key of the same table, and whose values sometimes match the respective primary key of same record. In this example, the absence of value (also known as NULL value) might be needed to represent an unrelated meaning: this tender can only be used at its full value.
Popular relational database management systems support this use case smoothly.
Take-aways:
When inserting a record, the foreign key reference is verified to be present after the insert, rather than before the insert.
When inserting multiple records with a single statement, the order in which the records are inserted matters. The constraints are checked for each record separately.
Certain other data patterns, such as those involving circular dependences on record level going through two or more tables, cannot be purely inserted at all, or at least not with all the foreign keys enabled, and they have to be established using a combination of inserts and updates (if they are truly necessary).