Anaconda Plan was to encircle the Confederacy and squeeze the Confederacy to death by cutting off all outsides trade.
The union Navy set up a blockade all along the Atlantic Coast to block trade. The Union conquered the gulf ports of New Orleans and Mobile to block trade along the Gulf of Mexico.
The Confederacy till was able to trade through Mexico across the Mississippi River. Vicksburg was the key to controlling the Mississippi River. As long as the South held the fortress of Vicksburg the south retained control of a least part of the River.
When Vicksburg fell enciclement of the Confederacyby the Anaconda plan was complete.
The fall of Vicksburg combine with the defeat at Gettysburg sealed the fate of the Confederacy