Like nodes, relationships carry different pieces of information. A relationship between two persons can be of type MARRIED_TO or FRIEND_WITH or many other types of relationship. That's why Neo4j's relationships must have one and only one type.
One of the main powers of Neo4j is that relationships also have properties. For instance, when adding the relationship MARRIED_TO between two persons, we could add the wedding date, place, whether they signed a prenuptial agreement, and so on, as relationship properties.
Be careful: even though we discussed undirected graphs earlier, in Neo4j, all relationships are oriented!