The Fulmination Discipline is lightning based, so it matches all of the artwork of Librarians surrounded by lightning storms. If you want you Librarian to play like Stormcast Eternals, it's the discipline for you. Oh, and it's pretty good too!
Electrosurge is the primaris power, and is a WC1 Witchfire. It is S5 AP4 Assault 6 with 18" range, so it's essentially 2 heavy bolters that can be fired on the move. It's not exciting, but it will do work for you against almost all armies.
Electroshield is a WC1 Blessing that gives the caster a 3+ invulnerable save. It's basically a psychic storm shield. While it would be more reliable to spend the points for a real storm shield, it's never bad to be able to give a character a great invulnerable save.
Electropulse is a WC1 9" nova power that hits every affected unit with a S1 Haywire attack. This is a good power in certain circumstances, such as if you can get the Librarian into an enemy parking lot of vehicles. However, this won't come up too often, so you'll mostly be casting it on one or two vehicles, wasting most of its potential as a nova power. It's not a bad power, but very situational.
Lightning Arc is a WC2 Witchfire with 18" range, S5 AP4 Assault D6 and Lethal Discharge. This means that every enemy unit within 6" of the target also takes D6 S5 AP4 hits on a 4+. While expensive to cast, this is a good power against infantry heavy armies, particular the MSU style armies which are becoming very common. It has excellent potential against most xenos armies as well as Imperial Guard and Adeptus Mechanicus.
Fists of Lightning is a WC1 Blessing that adds +1 to the caster's Strength and Attacks. In addition, every time he hits an enemy unit in close combat, it suffers two more S5 AP- hits. This really multiplies his hitting power by a deceptive amount. For example, a Libarian armed with a force sword and bolt pistol while casting this power will have 5 S5 attacks on the charge. Against most targets, 3 of these will hit (average number of hits is 3.33 against opponents WS4 or less). This adds six extra S5 hits for a total of 9. Not bad at all for a model with two base attacks!
Magnetokinesis is a WC2 Blessing that targets a unit within 18". As long as the target isn't Zooming, Swooping, or locked in combat, you can immediately move it up to 18", ignoring all intervening models and terrain. The unit can't assault that turn and counts as moving. This is a quick and reliable way to redeploy your units and is useful for grabbing objectives or getting your more mobile shooting units into range of juicy targets. For this, it's particularly useful with Sternguard and Centurion Devastators as they don't lose any firepower from moving and are fairly short ranged.
Electrodisplacement is a WC2 Blessing that switches the position of your psyker's unit with another friendly unit within 24". If either unit was locked in combat, the displaced unit is locked in combat as well. Otherwise, the units are allowed to charge this turn. This power is one of the new powers that made the biggest ripples in our community when it was released, as it allows first turn assaults. Generally, this means that you deploy your assault unit at the front of your deployment zone along with the psyker. Then either infiltrate, scout, or deep strike a unit next to your assault target. Switch places with Electrodisplacement and assault Turn 1.
In reality, I don't think this is really that huge, and the fervor over it has died down a but. Most real Space Marine assault deathstars are very fast and would be charging turn 2 anyway, and are durable enough to withstand a round of shooting with little effort. Paying for a Librarian and a unit to electrodisplace so that you can assault first turn if you roll the power (or buying enough Librarians to ensure you get the power) is expensive for marginal benefit. In addition, it's very easy to counter with some bubble wrap, something most good players of shooty armies bring anyway.
I actually like the inclusion of Electrodisplacement because it allows slower assault units to actually reach assault. Using it, Assault Terminators, Assault Centurions, and Honor Guard actually become viable without a Land Raider. I don't really see this army expansion happening in practice, but I think it would be fun and effective, though probably not tournament winning.
In conclusion, Fulmination is another strong discipline that is centered around close-ranged anti-infantry shooting and mobility. That's a very useful focus for Space Marines, which excel in close-up shooting and tend to be lacking in mobility. Sure, this is diluted by a pretty weak anti-armor nova, a decent but limited defensive spell, and a pretty strong assault buff, but Fulmination allows the Librarian and his unit to get into the enemy's face and do some damage when he's there.