Critically important. Artillery accounted for the most casualties sustained by all sides during the First World War and was employed as effectively in defence as it was in offence. German defence doctrine on the Western Front called for pre-designated Fire zones for German artillery batteries. In the event of a British or French attack, those batteries would fire on pre-ranged points, devastating any assaulting forces.

We can take the first day of the Somme as an example of how effective Counter-battery could be. Due to a lack of heavy guns, little counter-battery was undertaken by the British with the exception of those forces stationed at the most southern point of the British line, around the Montauban sector. Here, counter-battery operations were prioritised and with the help of French heavy guns, many of the German artillery batteries were successfully neutralised. Thanks to this, the assault on the Montauban sector was far more successful then anywhere else along the British Front. Of course there were other factors that contributed to this success such as the use of Creeping Barrages and local topography which favoured the British.

Now, how effective was it? This varied widely amongst the belligerents. The British were by far the best at it. Technological advancements such as Flash and Sound ranging, a scientific ranging method that, in the simplest terms, uses mathematics and trigonometry to measure the time between the sighting of a muzzle flash and the report of the gun, similar to how some people use a lighting flash and the sound of thunder to estimate how far away a storm is. Three such reports are used to triangulate the location of German guns. Once perfected, this became an incredibly efficient and effective means of locating German batteries.

Perhaps the first notable mass use of this technology was during the Arras Offensive at the beginning of 1917, especially during the Canadian assault on Vimy Ridge. During the preliminary phase, more then 80% of German artillery positions were located and successfully neutralised, tipping the balance of the battle heavily in favour of the assaulting Canadians. I should note that neutralisation doesn't necessarily mean destroyed, an artillery battery was deemed neutralised if it was prevented from firing. During the course of the war, this was achieved by killing the gun crews, killing the horses that made up the ammunition train and destroying railway systems that fed shells to the guns. During the Battle of Hamel, the German gun positions were smothered in gas shells, preventing them from participating in the battle.

I hope that answers your question, I just finished writing my Honours thesis on the effectiveness of Counter-battery operations and the use of Creeping Barrages.

Sources:

Battle Tactics of the Western Front by Paddy Griffith

The Killing Ground by Tim Travers

British Artillery on the Western Front in the First World War by Sanders Marble

Fire-Power: The British Army Weapons & Theories of War 1904-1945 by Shelford Bidwell and Dominick Graham