There are myriad of ways in which self-esteem and relationships are connected, in both positive and negative aspects. At first, a person's self-esteem can affect whether or not he or she is capable of finding a positive relationship in the first place. Then, interactions within the relationship can significantly affect an individual's self-esteem as well; again, in both positive and negative ways. In general, the connection between self-esteem and relationships is that people with higher self-esteem are more likely to find healthy, happy relationships, whereas those with lower self-esteem may have a more difficult time doing this, or may have a hard time sustaining relationships.
People who have a healthy level of self-esteem will often find that the connection between self-esteem and relationships is a positive one for a number of reasons. First, an individual with high self-esteem will have a good idea of his or her likes and dislikes and what she is looking for in a partner; she does not need to create herself based around another person. Second, people with higher levels of self worth tend to be happier and feel that they deserve the best in their lives, and will take steps to achieve this. Combined, these things add up to an individual who takes the time to seek out a healthy relationship, and has a lot to contribute to it when she finds one.
Individuals with high self-esteem are often better communicators as well. They feel secure in standing up for what they believe in, and don't tend to interpret everything as a personal slight. To many people, confidence is also a very attractive trait, which is another reason positive self-esteem and relationships often go hand in hand. Of course, the other side of this can be negative.
Someone entering into a relationship with low self-esteem might find that the relationship becomes one-sided, with one person making all the decisions. This is if he or she is able to find a relationship at all. In an abusive relationship where one individual is constantly verbally or physically abusing the other one, this can also have a severe impact on someone's self-esteem. Sometimes, people with especially low self-esteem will get into a vicious cycle in which they keep entering into bad relationships that perpetuate their low self-esteem. For this reason, it is important to understand the connection between self-esteem and relationships, and make sure it is a positive and beneficial one, rather than being a negative or damaging one.