In the real world, magnets interact in many entertaining and surprising ways, including cancellation: the creation of magnetic "dead zones" when multiple magnets are in close proximity. This works because the magnetic field at any point in space is the sum of the magnetic field from all individual sources -- so if one field points in one direction and the other points in the opposite direction at some point, the net field is zero.
However, as you can see in this example, the "dead zone" created by two simple magnets isn't exactly where you want it to be -- it's inside the angle they form. In addition, simple magnets have the unfortunate property that they have physical mass and cannot be perfectly superimposed. Thankfully, our increasing scientific understanding of electromagnetism has exposed us to magnets which suffer none of these limitations.* I refer, of course, to electromagnets.
The flow of electric current also generates a magnetic field. That means that by directing current in particular patterns, you can generate particular configurations of magnetic fields. One of the most common patterns calls for looping wire around a nonconductive core to form a "solenoid": a conductor which produces a magnetic field pointing straight in one direction (inside) or the exact opposite direction (outside).
So, "magic" is electricity, but conducted only by certain structures that have no physical mass (and preferably a minimum of direct interaction with mass, period). Where these structures loop tightly, resembling solenoids, magical force is generated -- and anything capable of interacting with (or being interacted with by) magic can convert that into power. The force is strongest inside the structure (along the ley line), has less energy outside, and drops off very quickly as you get further away. That force can be used to power the movement of stuff (teleporting people, crystal ball images, whatever) from one place to another, particularly if sent along a ley line. The simplest magical activity will involve simply sending things along with the current, pun fully intended. As practitioners becomes more sophisticated, they will develop ways to translate that raw motive power into other forms of energy, most notably mechanical energy -- the magical equivalent of a (living) electric motor which can power almost anything. Where two of these ley lines intersect, provided they are running in almost-opposite directions, the magical fields nearly cancel and we are left with a magical dead spot.
Now, before you stop with this simpler approach, think it through carefully: it has some implications. In particular, the political geography of your world will be weird. It's very likely that people in your world won't know why things don't transmit past ley line intersections, because much of the area around the dead zone will be hazardous or lethal for anything magnetic -- er, susceptible to magical force. So your magicians may not know that their spells fizzle in the intersection, because they'll be too busy avoiding the fact that their spells explode in the penumbra! If magical ability is an intrinsic gift that can't be turned off, it's even worse: normal people are able to travel freely while magically talented people may be hemmed in by the closest ley lines to their place of birth, unable to touch these invisible boundaries without suffering the same fate as a human who touches a live wire.
Moreover, ley lines based on this model are directional: perhaps a sending in one direction can work on the basis of the magician's power alone, but a sending in the other direction might require a wand and a rare gemstone placed in a certain configuration, the magical equivalent of a simple machine. Perhaps some forms of magic, such as lightning or telekinesis, naturally "flow" in the parallel direction if not deployed by a sufficiently skilled mage. Don't cast that fireball upwind!
If you're not a fan of these complications, or you want a more arbitrary ley line configuration, you'll need to add a few extra dimensions to your world so that the magical fields can run antiparallel in some dimension we can't perceive.** Magical fields no longer point along the ley lines; the ley lines are simply magical fields centered on some other 3+dimensional space that intersects with the 3-dimensional space we can perceive. (Strictly speaking, they're probably ley planes, but that doesn't have the same alliterative appeal.) The actual force vectors now point out of our space of existence.
To use magic, then, a magic-user reaches out (some possibly-immaterial part) perpendicular to their universe in higher-dimensional space so that the magical fields can act upon them, generating force which they can then channel to their own purposes. However, where these fields intersect (but point in opposite directions), there's simply no net magical field and thus no force can be generated no matter how the mage moves (unless they move within the visible universe -- i.e., leave the intersection).
Bonus: if ley lines are equivalent to higher-dimensional magnetic fields, you can introduce objects and people that look normal but have the properties of solid, static magnets and behave in wacky ways that are almost totally incomprehensible to the mere mortals who observe them.***
*Well, okay, maybe not none: a real electromagnet requires something to carry the electricity, and that conductor itself must have mass.
**To understand how this works, picture three planes superimposed. Leave one perfectly flat, slightly tilt one north/south, and slightly tilt the third east/west. The first is your world and the latter two are your ley lines. They run perpendicular from the perspective of your world, but in the higher-dimensional space they are very close to parallel -- and if they "point" in opposite directions, the fields will almost cancel where they intersect. Now repeat the visualization in three dimensions, and Bob's your uncle.
***NSFW for profanity. But come on, if you read through this whole post without expecting this joke…