An anxious attachment is a kind of emotional attachment in which a person possesses a negative view of him/herself and has a positive opinion of their partner due to which they develop a fear of losing their partner due to insecurity.
A person who is anxiously attached to the partner constantly seeks approval and assurance from their partner and requires intimacy.
A person who is anxiously attached is often encountered passing statements like "I find that others are reluctant to get as close to me as I would like." and thus constantly needs to be closer to their partner.
These people are always worried and anxious in their relationship and the statement given in the question reflects that the person passing the statement is anxiously attached.
