Rosh Hashanah, commonly known as the Jewish New Year, is a time to look back on mistakes of one's past and to plan changes to prevent making past mistakes again in the future year.
Working is not a permit-able action during Rosh Hashanah; the day is spent almost entirely in the synagogue studying a prayer book specially designed for this holiday called the machzor.
A common practice during this holiday is to eat apples dipped in honey, a treat symbolic of wishes of a sweet start to the new year ahead.
Yom Kippur is the most important Jewish year holiday, occuring only 10 days after Rosh Hashanah. It means "day of atonement," which is a day to "atone" sins that were of the last year.
Nobody is permitted to work during this holiday as most of the day's time is spent in the temple where the book of Jonah is read. The stories that are vocalized teach that no other person or being is beyond God's hand.
During Yom Kippur, its ordinary to see Jews wearing white as the color simply symbolizes purity and reminds them that their sins will be as replenished and white as snow. Others will otherwise wear a kittel-- a white robe people are buried in.