In 1984, there is a considerable age difference between Winston and Julia. Winston, for example, is thirty-nine years old while Julia is only twenty-six. This age difference is significant for a couple of reasons. First of all, because Julia is so much younger, she cannot remember life before the Party. When Winston talks about the Golden Country, for example, Julia has no understanding of what he means. This creates a contrast between their reasons for rebelling: Winston wants to recapture the past, before totalitarianism became the norm, while Julia simply rebels because it gets her the things she wants.
Secondly, the age difference has a rejuvenating effect on Winston. Julia's boundless energy and unquenchable sexuality energizes Winston, an aging man with a "varicose ulcer" on his leg. Arguably, it is her youthful enthusiasm which really drives their affair and, later in Part Two, drives them in to the arms of O'Brien.
In many cases, an older person comes to see life differently through a younger person's eyes. Young people usually do not accept the world as older people do. Young people are often idealistic and optimistic, and want to bring about change. Being around them can make older people want change again.
I would say that it is important because she energizes him in a way. Winston does have the guts to start the diary even before he meets Julia, but in a way he almost seems to have given up. She's so much younger and so much more vital than him and so she gives him a new sense of youth and possibility.