Jeanine, I am so glad you asked! Being that you harvested berries in September indicates to me that you have a fall-bearing variety. If you don't prune out the one year old canes/stems they will produce fruit the next summer/July. The new canes that are typically colored green will produce fruit in the September. 

In summary, fall-bearing varieties bear fruit on new canes, called primocanes. Summer-bearing varieties bear fruit on second year canes, called floricanes, which are typically brown colored. All of those two year old canes should be pruned out to ground level after they are finished producing fruit typically about August. Annual pruning is important to maintain a productive raspberry patch, including thinning out the canes when they become too dense. 

Here is a link to more details of growing raspberries: https://extension.umn.edu/fruit/growing-raspberries-home-garden#choosing-raspberry-plants-331662

Feel welcome to ask follow up questions, if I have confused you.

Paul -Master Gardener volunteer