Learn French: Le lit est mou, mais je voudrais un mol oreiller. - The bed is soft, but I would like a soft pillow.

Both words are masculine singular adjectives meaning soft. You use mou normally, like after the verb here. However, when the adjective comes directly in front of a masculine noun starting with a vowel or mute h (like oreiller), it changes to its vocalic form mol to make pronunciation smoother.

Doesn't the adjective for soft usually go after the noun? Why is it un mol oreiller instead of un oreiller mou?

You are right that physical qualities usually go after the noun. However, adjectives like mou and fou can sometimes precede the noun for a more poetic or subjective feel. Placing it before a vowel-starting masculine noun is exactly what triggers the special mol form. Note that saying un oreiller mou is also perfectly correct and actually much more common in everyday speech.

How does this mutation help the pronunciation flow of the sentence?

The word mou ends in a vowel sound. If you placed it directly before oreiller, you would get two vowel sounds clashing. By changing it to mol, the final consonant L is pronounced and links directly to the starting vowel in oreiller. This creates a smooth phonetic bridge and avoids an awkward pause.

Why use voudrais instead of veux here?