The self-reference effect is a tendency for people to encode information differently depending on the level to which the self is implicated in the information. When people are asked to remember information related in some way to the self, the recall rate can be improved.

Research suggests that self-structure is unique, relative to other concepts (e.g., those about other people; see Kihlstrom et al., 1988; Markus, 1977; and Rogers, Kuiper, & Kirker, 1977), in its motivational and affective implications as well as in its structure and content. Appraisal theories of emotion have emphasized the phenomenological importance of the self in the interpretation of events and the resulting effect on emotions (Fiske & Taylor, 1991 ).

Example, the tendency to attribute another person's behavior to dispositional factors but one's own behavior to situational factors occurs because the self dominates one's phenomenal perspective (Ross & Nisbett, 1991; Storms, 1973).

Brain regions associated with self-reference effect

1. Cortical mid-line structures: A quantitative meta-analysis that included 87 studies, representing 1433 participants, uncovered activity within several cortical midline structures in activities in which participants performed tasks involving the concept of self. Most studies that report such midline activations use tasks geared towards uncovering neural processes that are related to social or psychological aspects of the self, such as self-referential judgments and self-appraisal.

2. Prefrontal cortex: During various functional magnetic resonance imaging(fMRI) tests conducted while participants were performing self-referential tasks, there was a consistent showing of increases in Blood-oxygen-level dependent (BOLD) signals in the ventral medial and dorsal medial prefrontal cortex.

3. Parietal lobe: During fMRI given during self-referential tasks there also appeared to be increases in BOLD signals within the medial and lateral parietal cortex. When participants were subjected to transcranial magnetic stimulation over the region it decreased the ability of participants to retrieve previous judgments of mental self when compared to the retrieval of judgment of others.

Development of self-reference effect over lifespan

• Childhood: Research focusing on recall abilities of children show self-referencing advantage in children as young as five years old. Language development appears to play a significant role in the development and use of the self-reference effect. 
• Adulthood:  Theories of intimacy and personal relationships suggest that self-reference effect is affected by the closeness of a relationship with the other used as a target. The capacity for utilizing the self-reference effect remains relatively high throughout the lifespan, even well into old age. Older adults exhibit increased recall when using self-generated strategies that rely on personally relevant information (e.g., important birthdates) relative to other mnemonic strategies. 

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Self-reference effect refers to the tendency of a person to better remember information when it is in some way related to the person. Three parts of the brain viz. cortical mid-line structures, prefrontal cortex and parietal lobes play a role in the self-reference effect. It has been found to start as early as the age of five and continue throughout the lifespan, becoming stronger compared to other mnemonic methods as a person grows old.

Sources:
http://en.wikipedia.org/wiki/Self-reference_effect
The Self-Reference Effect in Memory: A Meta-Analysis by Cynthia S. Symons, Blair T. Johnson