For the purpose of the ITIL 4 exam, you do need to understand the purpose of relationship management and memorize this definition. The purpose of relationship management is to establish and nurture the links between the organization and its stakeholders at strategic and tactical levels.
This is done by identifying, analyzing, monitoring, and doing continual improvement of those relationships between various stakeholders. The most common of these relationships is the one between the service provider and the service consumer. For example, in the food industry, the restaurant is the service provider and you're the service consumer. The restaurant wants to make sure that you're happy. They want to make sure that your needs are met. And by understanding all of that, and having a proper relationship between the restaurant and you, they are hoping that you're going to go and eat more frequently from them, and that you're going to be happy about your meal and experience at their establishment so you'll go and tell all of your friends. If that happens, then the restaurant has some good results that have come out of this relationship management practice.
Now, when looking at this about stakeholders at the strategic and tactical levels, it's not just service provider and service consumer though. There are a lot of other ones in there. As you're going through and building those relationships, you need to monitor those relationships. Identify the needs of those relationships. What exactly does that stakeholder need? There may be a stakeholder who is asking for a new product or service. As part of relationship management, you're going to talk to them and identify exactly what all of those needs are that they have. Put that into your requirements and figure your "how we're going to build those things". As you do that, you're going to monitor that and make sure that you're meeting all the things you needed to, and then make sure that it's done properly. Then you'll go through continual improvement to make that go through again and get it better than it was before.
The whole idea with relationship management, again, is to establish and nurture the links between the organization and its various stakeholders at strategic and tactical levels. If you remember that for the exam, you're going to do great.