What does it mean when Pride mentions about Edward turning into a philosopher's stone to infiltrate him?
You have to remember that philosopher's stones are merely the souls of people.

I haven't watched the episode in a while, but I'm fairly certain Edward explains it as using part of his own soul/life force to generate a philosopher's stone.

Edit: found this on the wiki


  Breaking free of his bonds, Edward takes hold of Pride's head and, turning himself once more into a single-souled Philosopher's Stone, forces his way into the Homunculus' psyche.