i enjoy picking fruit.  fruit picking is a season activity that occurs during the harvest time in areas with fruit growing wild or being farmed in orchards
What is considered harvest time?  Is it just a set time every year?
it really just depends on the type of fruit you are picking.  they also have harvest festivals that are annual celebrations that occur around the time of the main harvest of that region
That is neat.  So what types of fruits are picked?  
Apple picking is a big fruit in the US.  Apple orchards are even open to the public in some areas that allow customers to pick their own apples or they can also purchase pre-picked apples
Are there certain parts of the US that are especially known for their apple orchards?
Yes, apple picking is very popular in the midwest of the united states of america
Is that also were apple cider comes from?   I really enjoyed drinking that as a kid.
well it does come from apples! cider is basically unfiltered, unsweetened, non-alcoholic beverage made directly from apples.