According to PBS, there were two main causes of the stalemate during WWI: the failed military tactics of The Schlieffen Plan, and the new war tactics required for trench warfare.
The Schlieffen Plan was initially perceived as flawless and strategic, and its purpose was to gain victory quickly for Germany. The plan was designed to calculate exactly how many units Germany would need to secure victory over France by way of Belgium, but it failed when the German general Moltke sent too few troops to invade Belgium. Germany hadn't expected France to find an effective defensive strategy or for other countries to come to France and Belgium's aid.
The second aspect, trench warfare, began in November of 1914. There was a total of 12,000 miles of trench by the war's end. The Allies and Central Powers had approximately 6,250 miles of trench by the end of 1914. The trenches prevented movement on both sides as the land between trenches was covered in barbed wire and booby traps. The addition of machine guns and long-range rifles made movement impossible in these areas. Attacks generally occurred in the early morning hours since poisonous gas thrown into trenches was more effective in the cold, windless air.