It shows a pattern of responsibility.
If you have only had accounts for 1 month, it doesn't really give a full picture of whether or not you always make your payments on time, etc. However if you have had accounts for 20 years, creditors have more history to look through to determine if you are responsible.
Keep in mind, checking and savings accounts are not the primary type of accounts that creditors want to look at because those only deal with spending money you already have. Lenders really want to know how you handle money that you borrow, such as school loans, credit cards, rent payments, and auto loans.