Leylines are areas which increase the spell power of spells by mages and shamans. In SR games, they are represented by circles of three different sizes. All leylines will increase the accuracy of spells when attempting to hit enemies.
Large leylines have the greatest potential to supercharge your spell wielder, as they can reduce the cooldown of spells and allow them to affect multiple targets. Spells with 1 turn cooldown can be casted repeatedly in the same turn as long as the caster has AP. Thus, a mage with 3 AP standing in a large leyline can cast Aim to benefit the whole party and then cast Shred Armor twice to decrease the armor of multiple enemy targets. However, note that for offensive spells, the increased spell power from leylines can be a double-edged sword, as such spells often do not discriminate between friend and foe.
Another point about leylines is that they are often found away from cover. This means that the caster should be protected via other means, or other party members should help draw fire away from the caster.