Client Side Encryption is the idea of having messages encrypted within the client application before they are sent to a server.
This is often confused with services that use SSL connections (i.e HTTPS) and call themselves client side encrypted. SSL is simply a protocol used to encrypt data while it is sent over a network and prevents very basic snooping techniques such as listening to a WI-FI network or hacking a router. However, this DOES NOT PREVENT any attacks that can occur on the server that received the data. The server still owns the information.
With real Client Side Encryption, data is encypted by the client application and thus cannot even be accessed by the programmers of the server. This method means no one with access to the network or the server can access it. The server does not own your information, the user owns the information.
You can find more technical information over here.