The term Intergenerational relationship has been used in different ways. These can be simplified to two distinct usages:
A generation loosely defined is the period of time it would take for a new-born child to reach the age of legal majority, or, depending on the culture - the age at which they can legally procreate. A "generation" therefore is usually defined as roughly 20 years.
An intergenerational relationship is a relationship that spans this gap, for instance, an 18yo man having a relationship with a 40yo woman. It can be considered taboo, although there are no laws against such a relationship.
The other use is not really related to the term "generation" but rather the divide of the legal Age of Consent. An "intergenerational relationship" in this sense therefore could be defined as any adult who has an intimate ongoing relationship with a child. The adult would only need to be 5 or so years older than the child for this definition to be correct.
This kind of relationship is highly controversial and illegal in most western countries. This is mainly due to the concept that before the age of consent has been reached, a "child" does not have sufficient capacity to make decisions that adults in the same kind of intimate relationship would, and therefore this leaves the balance of power clearly in the hands of the older adult.
It must be stated however that is should never be used to judge a personal choice such as a relationship. Each person's level of maturity is different, and therefore also the amount of responsibility they can handle, this is without going into the concept that the older adult may not actually abuse this power - as the main argument against Intergenerational Relationships seems to miss this fact - namely, if an adult has the control, it does not follow that they will misuse this to their own advantage - and common sense would dictate if they truly did love the other person (as would be a pre-requisite of such a relationship) - then most likely they would use the imbalance to the minor's advantage.
However, due to the culture of fear and Pedophobia, intergenerational relationships of the second type are still "anathema" and both parties are put at risk of both law and vigilante justice simply due to one party's age.