A very simplified explanation of compression ratio is the amount the air/fuel mixture in the cylinder is compressed. In the case of a 10:1 compression ratio. The air/fuel mixture is compressed to 1/10th of it's original volume.
The more the air/fuel mixture is compressed, the easier it is to detonate. Higher octane fuels avoid pre-ignition and potential engine damage.
Generally, higher compression ratios result in a more efficient engine both in economy and performance. The only penalty is the cost of the higher octane fuel.
BTW, many brands of gasoline have a higher level of additives in their premium fuels. This is true with Chevron and Amoco among others.