To quote Winston Churchill, "In the West, the Armies were too big for the Land. In the East, the Land was too big for the Armies."
The distances were simply too great to permit static, trench warfare; there was not a high enough concentration of troops on both sides to allow that. There were periods in which the armies dug in, but these were mostly thinly held 'outpost lines', with larger battalions ands regiments holding villages as strongholds further behind the lines, essentially the same in WWII. Cavalry was widely used, and great, mobile operations, like the Battle of Lemberg and the Capture of Lodz in 1914, the Gorlice-Tarnow Offensive and the Great Retreat in 1915, the Brusilov offensive and the Invasion of Romania in 1916, the Kerensky Offensives and the Battle of Riga in 1917, and Operation False Flag in 1918, were common place.
Timothy Dowling, "Brusilov Offensive"; Geoffrey Wawro, "Mad Catastrophe"; Max Hastings, "Catastrophe"; Peter Hart, "Great War: A Combat History of the First World War"; Alexander Watson, "Ring of Steel"; Hew Strachan, "First World War, Volume One: To Arms!"