Damage to marble such as you describe can be caused by vinegar. Vinegar will "cut" many minerals, including marble.
Somebody may have used vinegar to try to clean the marble. (It works great on glass.)

What can be used to get the shine back?

your local home center will have a marble floor finish sealer (hi gloss finish will be available)

i saw this on home depot's website can i use it to get the shine back ....TILELAB®
STONEGLOSS™
POLISH

• Shines polished marble and stone
• Hides etching and abrasions
• Helps protect against spills and stains
PRODUCT DESCRIPTION
Water and stain resistant, spray and buff polish for polished stone. Restores luster and enhances color while hiding etching and abrasions. Provides water-resistant finish.

USES
For all polished stone such as marble, terrazzo, serpentine, limestone and granite.

DIRECTIONS
Shake well before using. Spray a light, even mist and spread with a clean, dry cloth. A small amount is all that is needed. Allow to dry until a haze forms. Then buff surface to a shine with a clean, dry, soft, lint-free cloth. Not recommended for floors. For maximum stain protection, seal stone surface with TileLab® SurfaceGard® Penetrating Sealer.