What are the key chemical characteristics that determine the octane rating of fuel?
Combustion
 is (usually) chain radical reaction with heavy branching. More 
branching means faster combustion and less branching is slower 
combustion. And detonation is wave of super-fast combustion.

So, if you can suppress branching or deaden some branches, you can 
increase durability of air-fuel mixture. Actually, this means, that some
 radical trap is needed. The oldest trap was tetraethyllead, but it is 
currently dropped (lead oxides as fine dust is not a health friendly 
substance). Non-saturated hydrocarbons of different types also can trap 
active radicals, transforming them into more stable allyl radicals, so 
fuel companies tries to keep as much of them in fuel as possible. Some 
other compounds, like ferrocene, also can be used to increase octane 
rating.