Learn Russian: Это мой матрас, нельзя ложиться на него. - This is my mattress, you cannot lie down on it.

In Russian, verbs that describe assuming a position (like ложиться, to lie down) are treated as verbs of motion. You are moving your body onto a destination. Because of this directed motion, we use на + the Accusative case. If you were already resting on the mattress, you would use a different verb and the Prepositional case (лежать на нём).

Why is the imperfective verb ложиться used here instead of the perfective лечь?

The word нельзя can mean either 'it is forbidden' or 'it is impossible'. When it means 'forbidden' or 'you must not' (as a rule), it is almost always followed by an imperfective verb like ложиться. If it meant it was physically impossible to lie down, you would use the perfective лечь.

Why does the pronoun have an 'н' at the beginning (на него) instead of just being на его?

Whenever a third-person pronoun (like его, её, or их) comes directly after a preposition (like на, в, or с), Russian adds an н- to the beginning to make it easier to pronounce. Since матрас is a masculine noun, we use the masculine accusative pronoun его, which becomes него after the preposition на.