Today's high performance engines typically have high compression ratios and/or turbochargers, either of which necessitates higher octane gas. Octane's a rating based on the measurement of gasoline's resistance to pre-ignition or "detonation" which is when the air/fuel mixture in a cylinder burns during the wrong part of the combustion cycle, resulting in a "ping" sound. Severe detonation can cause engine damage in the form of cracked or melted pistons, broken piston ring lands, bent rods, etc.
The measurement methods used can differ. Europe uses the RON method whereas the USA, Canada, and some other countries use the R+M/2 method. What's called "98 octane" in Europe is roughly equivalent to "93 octane" in the USA. But there's more to it than that. Additives like detergents, oxygenated fuel, ethanol mixtures, etc can also have an effect on how gasoline burns. In California and most of the rest of the west coast the highest octane available at the pump (with the exception of racing and aviation gas) is 91 octane and the lowest is 87. In much of the rest of the USA it's 93 octane, occasionally 94. My car runs like shit on California 91 octane. I have to mix in 1/4 of a tank worth of 100 octane race gas to keep it from pinging at full throttle.
For a lawnmower engine I would imagine 87 octane would be totally fine unless you're at a high altitude.
