When you talk about timers and resolution, what do you actually mean? When I hear timer, I think about setTimeout, when I hear resolution, I'm thinking about screen resolutions.
Is that what you mean, or are you referring to other things?
Resolution is the precision that the timer reports the time. For example, it could report seconds elapsed (e.g: 8 seconds), it could report milliseconds (8.432 seconds), it could report microseconds (8.432389 seconds), etc.
Attackers want high resolution timers so that they can distinguish cache hits from misses (8.432389 seconds vs 8.432367 seconds, for example).