What type of interaction is depicted by the dashed line?
The image is slightly misleading in that the interaction is actually between the second carboxylate oxygen and one of the amine hydrogens.
It is in part a hydrogen-bonding interaction, where the carboxylate oxygen is the hydrogen-bond acceptor, and the amine hydrogen is the donor.
It is also an ion-pairing interaction, between the partially-positive hydrogens as a group and the partially-negative oxygen.
Electrostatic Physical Bond. As shown, most likely 'Hydrogen-Bonding' between electronegative nitrogen and the electropositive carbon center of the carbonyl carbon of the carboxyl group.
There are three types of bonding in nature; physical, chemical and nuclear bonds. Physical bonds are weak electrostatic interactions (i.e., +/- attractions) between elemental structures. Chemical bonds are strong interactions from ion interactions or electron orbital interactions. Nuclear bonds are the strongest bonds involving neutron/proton/electron interactions at the nuclear level.
Within the 'Physical Bonds' classification is the 'Hydrogen-Bonding' which is a special case of dipole-dipole interaction between highly electronegative N, O, or Halogen (F, Cl, Br. I) in which one of the interacting elements is also covalently bonded to a highly electronegative element. By convention, this is typically represented by a dotted line between interacting elements.