Learn Spanish (Latin America): El gran valor sentimental de esta foto no lo comprendes. - The great sentimental value of this photo, you do not understand.

This is the core of topicalization (left-dislocation). When you move a direct object to the front of a sentence to emphasize it, Spanish requires you to repeat that object with a matching pronoun before the verb. Since valor is a masculine singular noun, we use the pronoun lo.

Is it grammatically correct to just say No comprendes el gran valor sentimental de esta foto?

Yes, that is the standard, neutral word order. Moving the object to the beginning of the sentence is a stylistic choice used to highlight the topic of the conversation. It translates closely to the feeling of saying 'As for the great sentimental value of this photo, you don't understand it.'

Why is the adjective gran placed before valor, and why isn't it grande?

The adjective grande drops its final syllable and becomes gran whenever it is placed directly before a singular noun, whether masculine or feminine. We place it before the noun here because it carries a subjective, figurative meaning (a great value) rather than a literal physical size (a big value).

Why does the negative word no appear in the middle of the sentence instead of at the beginning?