What is the psychology behind the need to be the centre of attention? In conversations, there are often times when a member of the group will consistently divert the conversation back to their own topic (often to do with them).  A 'pseudo-conversation' example:


Persons 1-3 are talking about A - going back and forth as
conversations often do.
Person 4 starts talking about B - a topic about them
Persons 1-4 talk about B for a bit, and that part of the conversation
is largely concluded.
Persons 1-4 talk about A again (as it had not concluded) - picking up were they left off.
Person 4 starts talking about C - another topic about them, loosely related to topic B


(Note: for these examples, topics A, B and C are not urgent).

Many people seem to do it without realising, some habitually do it - but, it seems commonplace. 

The question is, what is the psychology behind the need to be the centre of attention?
Depends on the pattern of how this occurs -- the situation, consistency, and severity.

If across situations, across different other people, and across different settings, this would indicate a personality trait. The person might be unaware of the social cues of others and draw attention to ideas that are interesting to them. Most people are interested in talking about themselves. Combine this tendency with lack of awareness, and you might see what you're describing.

If they consistently dominate the group conversation across different people and different situations, to the point where the pattern negatively affects their life or work, they might have a narcissistic trait or even NPD. In such case, the person's concept of self-worth may be abnormally modulated by the positive attention they receive from others. They might have a need to be the focus of attention, because otherwise they may feel degrees of worthlessness. This need may have developed during childhood from one or a series of traumatic events (i.e. narcissistic parent).

If this happens consistently only with one group of people, it could be that the people in the group consistently have conversations that are uninteresting to the person. 

Additionally, the group of people might be meeting in a certain place or a certain time, during which the person might be more likely to want to talk about themselves. Perhaps, the group meets after the person has finished their soccer practice, or after a weekly meeting with their boss. If so, the person might be particularly excited to talk about their game events, or how pressured they feel at work.