We must capture Vicksburg so that we can take control of the entire course of the MIssissippi RIver and thus isolate Confederate States that lay west of the river from those in the east. Getting Vicksburg is they key to winning the Civil War!
We can't let the Union take control of the entire river! We must defend Vicksburg because if they capture it we will be unable to send supplies or communications across. Our armies would be divided! If we let them win we won't be allowed to become a separate country.
The Union had a much larger army and more industrial resources.
The Confederate States had a weak army and had shortage of supplies and resources.