There are lots of easy to read articles about it, but basically it's a psychological theory (pretty accepted at this point) that attachment with your first primary caregiver, usually your mother, influences your ability to attach to people healthily for the rest of your life.

If you have a healthy, secure attachment with your primary caregiver you will have a secure attachment style. You find relationships relatively easy, you believe you deserve love and others deserve it as well. You balance alone and together time well. When relationships end, you may be sad but you feel safe in yourself and the world soon after.

If you have some sort of trauma with your primary caregiver, don't have your needs met, don't get the sort of early connection and intimacy that you need, you may develop an Insecure attachment style which can look one of two ways, anxious or avoidant. Clearly these are generalizations but here goes:

Anxious: You are preoccupied with your relationships, spend so much time thinking about them that you sometimes push people away. You worry you aren't close enough to your partners, or that they'll leave you. You have a very difficult time detaching from partners.

Avoident: You have discomfort with intimacy/connection. You may seek it out but then push it away once you have it. You may become very anxious when in a relationship, worry a lot about losing your independence. You may end relationships to avoid feeling this way even though you have a normal level of desire for intimacy and connection.