When you remove a friend on Snapchat, they will be removed from your friend list and will no longer have access to your Snap Map location. They will also not be able to view any of your private Stories or Charms, but they will still be able to view any content that you have set to public. Depending on your privacy settings, they may cease viewing your stories and Cameos Selfies. They will lose access to your Snapchat points, often known as Snapscore. Even if you were having a live chat with them, all of their Snaps would be marked as Pending. They would still be able to look you up, but they would have access to only a portion of your profile. Finally, just because you removed somebody from your friend list doesnt mean they removed you from theirs.
It is important to note that Snapchat does not notify users when they are removed from someones friend list. However, if you add them back, they will be notified.