Yes. SpiderOak encrypts your data at every stage in the process -- from uploading to storage to downloading again. This process ensures complete security and privacy at all times.
SpiderOak is a No Knowledge backup provider. This means that we do not know anything about the data that you store on SpiderOak -- not even your folder or filenames. On the server we only see sequentially numbered containers of encrypted data.
Please note that No Knowledge applies only when using the SpiderOak client. When logging into the website with your password, you are giving the primary encryption key to our servers. We work hard to ensure that this key is kept safe (for instance, by only keeping it in memory and never writing it to disk), but to maintain absolute privacy, you should use only the client.