There are at least two ways in which to answer this question. First, we can say that Fort Sumter is important because it was the site of the action that touched off the Civil War. Second, we can discuss why Fort Sumter was important enough that the North and South fought over it.
On April 12, 1861, Confederate forces in Charleston, South Carolina opened fire on Fort Sumter. The fort was manned at that time by a small force of US military personnel. This was the first time that actual fighting had broken out between the US and the Southern rebels who had seceded from the Union. Up until that point, it was at least plausible to think that the US and the CSA could avoid a war. After the CSA fired on Fort Sumter, war was essentially inevitable. Therefore, we can say that Fort Sumter is important because it was where the Civil War began.
But why did the Civil War begin there? What was so important about Fort Sumter? Some people might say that Fort Sumter was important because it commanded Charleston harbor. That is, it was located in a place where guns in the fort could destroy ships trying to enter or leave the harbor. This meant that it was dangerous to the Confederacy. However, this argument really does not hold up. The fort had never been completed and had very few guns and not much ammunition. It could not really threaten shipping very much. More importantly, the fort had been designed decades before and was not strong enough to withstand modern artillery. This meant that the CSA could easily destroy it whenever they wanted. Therefore, Ft. Sumter was not militarily important in the condition it was in on April 12, 1861.
What was really important about Ft. Sumter was its symbolic value. The fort was occupied by the Union right in the middle of the Confederacy’s main harbor. This looked very bad for the CSA. It made them look as if they did not even control the territory that they claimed to control. This is why they needed to attack Ft. Sumter. They needed to demonstrate to the European countries (and perhaps to their own people) that they were actually in control of the territory that they claimed. It was for this reason that the CSA attacked Ft. Sumter and the Civil War began there.