Traditional Linear Secret Sharing Schemes (LSSS): It’s a way to split a secret into pieces so that only certain combinations of those pieces can reveal the original secret.
Good for simple math: LSSS works well for adding or multiplying secret numbers without anyone actually knowing the numbers themselves.
The Catch: LSSS requires everyone involved to be online and communicating at the same time. This can be inconvenient in the real world 
The Nillion’s Non Linear Operation: Nillion handles complex calculations on hidden information.
Non interactive computation: Pre processing is done in advance, so the actual computation doesn’t require parties to be online simultaneously. 
Benefits: This eliminates the usual slowdown of parties having to talk to each other while calculating thus increasing speed and efficiency.