まま attached to Vた or Nの indicates that the described state is left unchanged. It often implies that the state is contrary to what is usually expected. そのまま is used to take up what has been described in the preceding sentence.
その電車は止まりました。そのまま、動きません。
That train stopped. It remains as it is, and does not start moving again.
その電車は止まったまま、動きません。
That train stopped. It remains as it is, and does not start moving again.
電気をつけたまま、ねました。
I went to bed, leaving the light on.
くつのまま、へやに入らないでください。
Please don't enter the room with your shoes on.
皮のまま、りんごを食べましょう。
Let's eat apples without peeling them.