On Yom Kippur God showers the world with forgiveness. But just like a shower if you want to get clean you have to get into the water!
'Getting into' Yom Kippur, however, is easier said than done. We earthlings relate to things that are tangible, i.e., french fries and phone bills. Spiritual matters - the commanments, the World to Come, repentance, etc. - are harder for us to get excited about.
Therefore we have Rosh Hashana first. On Rosh Hashana all our physical needs are determined. Will we live or will we die? Will we have money for the phone bill? Once we begin thinking about these issues, asking God for a year of health and wealth, we can then hopefully go one step further and ask forgiveness and for help in following the way of the Torah.
May we all be written and sealed in the Book of Life!