Good telegram question by TYC: How do side-chains maintain the integrity of blockchain transactions if they are not on the chain?
Answer by Guy Zyskind: There are different ideas out there. Side-chains (or child chains, or whatever nomenclature people agree on) usually also have consensus, but the thought is that they are often secured by less nodes/computational power and are therefore less secure.
Plasma added the general idea that you can add exit conditions to a chain higher up the stack (kind of like disputing from a regional court to a supreme court). The details are still in flux and the general proposal has evolved into many more refined ones, but the idea is the same.