Final answer:
The Union successfully laid siege to Vicksburg, gaining control of the Mississippi River.
Step-by-step explanation:
The significant event that occurred during the Battle of Vicksburg in May-July 1863 was that the Union successfully laid siege to Vicksburg, gaining control of the Mississippi River.
The Union forces surrounded the city, blockading it, and cutting off its supplies. Union troops dug trenches to move closer to the Confederate battlements, and Union artillery shelled the city. The Confederate forces, under siege and facing starvation, surrendered to the Union, giving them control of Vicksburg and effectively splitting the Confederacy in two.