or is used to connect two possibilities, for example
Would you like tea or coffee?
In this context, it is considered to be dating violence if it it carried out by somebody who either
is in a social relationship... - the relationship is current
or
has been in a social relationship... - the relationship is no longer current
The difference between was and has been is that we use simple past was when talking about something that occurred in the past at a specified time, and we used has been when we are talking about something that occurred at an unspecified time in the past, but it is considered to have some lasting effect.
The attacker was in a relationship at the time of the attack -simple past
The attacker has been in a relationship -present perfect
In that second sentence, it is not specified when the attacker was in a relationship, but it is considered significant to the attack.