This is best demonstrated by example.
Let's say you have three cards, and the older two you don't use any more. The cards are currently 5, 3, and 2 years old (max age 5 years, average age 3-1/3 years).
If you leave them open, next year, you'll have a maximum age of six years, and an average age of 4-1/3 years.
If you leave them open for five years, you'll have a maximum age of ten years, and an average age of 8-1/3 years.
Let's say you closed the older two now. Average age seems to count more heavily for open accounts, so your age would drop to 2 years.
In five years, your maximum open account would be 7 years old, and your average age would be 7 years.
For a more complicated example, let's say you opened a new card in year 4 and we're looking at year five.
All four accounts open: max age: 10 years, average age (10 + 8 + 7 + 1)/4 = 6.5 years.
If you'd closed the two older accounts: max age 7 years, average age (7 + 1)/2 = 4 years.
While it might not seem like a lot, 10 years is 43% longer than 7 years. 6.5 years is 63% longer than 4 years. These do translate to score differences.