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Gram-positive bacteria are those that are stained dark blue or violet by Gram staining. This is in contrast to gram-negative bacteria, which cannot hold the crystal violet stain. Instead they take up the counterstain (safranin or fuchsine) and appear red or pink.
The difference is caused by the cell wall structure. Gram-positive organisms have thick peptidoglycan layer. This protects them, so they do not need rigid cell walls. On the other hand, gram-negative bacteria have thin, insignificant peptidoglycan layers, so they do need rigid cell walls for support and protection.