We're talking about RMU here to be clear (since this forum is for all versions of RM).
The spell being dispelled needs to make its RR by beating the spellcasting roll (because this is how all RRs vs spells work). The spellcasting roll was successful if it was at least a 1. So, if the Dispel was cast with a very low spellcasting roll, it will be easy to make that RR. If Dispel was cast with a very high spellcasting roll, it's quite hard to make that roll.
To... ahem... spell it all with an example:
Vedran is an 8th level magician with 13 ranks in Dispelling Ways, with a total SCR bonus of +33 in that list. He encounters a giant octopus which he suspects is actually an illusion. In fact, he is correct; it's a phantasm cast by a 10th level illusionist. He casts Dispel Essence I (a 4th level spell), and rolls a 12, getting a total of 45. The dispel is successfully cast, now the phantasmal octopus makes a RR. It rolls a 50, and then to take into account the respective casting levels the phantasm gets +20 (it was cast by a 10th level character) and the dispel penalizes it by -16 (it was cast by an 8th level character) for net level modifiers of +4, and the total roll is therefore 54. That beats 45; the phantasm does not waver. However Vedran is seeing attacks go harmlessly right through the octopus, and it's not dealing any damage, so he's sure of himself and casts another Dispel Essence I. This time he rolls a 60 for a total SCR of 93; the phantasm rolls 42 +4 for a total of 46. The octopus vanishes.