"Adult attachment styles" is a fancy phrase for the way people interact, physically and emotionally, in intimate relationships. These attachment styles are characterized as secure, insecure (often called anxious-resistant), or avoidant.
In a secure attachment between two adults, each is confident that their partner is trustworthy and that the other loves them and will be there for them when needed, even if temporarily separated by time and distance. Those in the secure category can easily develop healthy dependencies and allow themselves to be depended on by others without fearing abandonment or being infringed upon. Appropriate boundaries in both friendships and romantic relationships are the norm.
Insecure attachment denotes those adults who have moderate to extreme anxiety when their partner is not present or perceived to be unresponsive to their needs. For these people, even a return of the partner or a change to responsiveness will not immediately soothe their distress. This attachment style is characterized by intense fear of disapproval and abandonment and the desire to bond tightly to their partner, often overwhelming and pushing the other person away. Variations would include acute jealousy over other relationships in their partner's life, and insistence of knowing where they are and what they're doing at all times.
The avoidant attachment is similar to the insecure attachment in that the root of the emotional stressors and fears are the same. However, while the insecure attachment will focus on their own perceived inadequacy ("I am afraid s/he won't love me or will leave me") the avoidant attachment sees others as the problem ("Others are not trustworthy, so I will not depend on them"). Consequently, this attachment style tends to push others away from the start, feeling uncertain and therefore, avoiding the entire relationship altogether.
Interestingly, extensive research has shown that these adult attachment styles parallel the observed attachment styles in infant-caregiver relationship. The percentage of occurrence of each attachment style is approximately the same in infants and adults; 60% are secure, 20% are insecure, and 20% are avoidant. This begs the question of whether the attachment style we exhibit as adults is a direct result of the style modeled to us as appropriate when we were infants.
Regardless of how each adult attachment styles come about, understanding your style and your partner's - can bring insight into your close relationships with friends and romantic partners.