What is "vital formations"? In this answer by @yuttadhammo, he quotes a section of the Visuddhimagga:


  After reciting the Pātimokkha, it seems,
  on the Uposatha day of the full moon, one of the two elders who were brothers
  went to his own dwelling place surrounded by the Community of Bhikkhus. As
  he stood on the walk looking at the moonlight he calculated his own vital
  formations, and he said to the Community of Bhikkhus, “In what way have you
  seen bhikkhus attaining Nibbāna up till now?” Some answered, “Till now we
  have seen them attain Nibbāna sitting in their seats.” Others answered, “We
  have seen them sitting cross-legged in the air.” The elder said, “I shall now
  show you one attaining Nibbāna while walking.” He then drew a line on the
  walk, saying, “I shall go from this end of the walk to the other end and return;
  when I reach this line I shall attain Nibbāna.” So saying, he stepped on to the
  walk and went to the far end. On his return he attained Nibbāna in the same
  moment in which he stepped on the line.
  
  -- Vism. VIII.244 (Nyanamoli, trans)


I'm echoing @Parag's inquiry, from the comments, here: what is meant by "vital formations" above?
Here is a quote from "The Majjhima Nikaya 43 - Mahavedalla Sutta: The Greater Series of Questions and Answers" that explains the term "Vital Formations":


  VITAL FORMATIONS
  
  
  "Friend, are vital formations states of feeling or are vital formations one thing and states of feeling another?"
  
  
  "Vital formations, friend, are not states of feeling. If vital formations were states of feeling, then when a bhikkhu has entered upon the cessation of perception and feeling, he would not be seen to emerge from it. Because vital formations are one thing and states of feeling another, when a bhikkhu has entered upon the cessation of perception and feeling, he can be seen to emerge from it."
  
  
  "Friend, when this body is bereft of how many states is it then discarded and forsaken, left lying senseless like a log?"
  "Friend, when this body is bereft of three states - vitality, heat, and consciousness - it is then discarded and forsaken, left lying senseless like a log."
  "Friend, what is the difference between one who is dead, who has completed his time, and a bhikkhu who has entered upon the cessation of perception and feeling?"
  
  
  "Friend, in the case of one who is dead, who has completed his time, his bodily formations have ceased and subsided, his verbal formations have ceased and subsided, his mental formations have ceased arid subsided, his vitality is exhausted, his heat has keen dissipated, and his faculties are fully broken up. In the case of a bhikkhu who has entered upon the cessation of perception and feeling, his bodily formations have ceased and subsided, his verbal formations have ceased and subsided, his mental formations have ceased and subsided, but his vitality is not exhausted, his heat has not been dissipated, and his faculties become exceptionally clear. This is the difference between one who is dead, who has completed his time, and a bhikkhu who has entered upon the cessation of perception and feeling."
  
  -- The Middle Length Discourses in the Majjhima Nikaya, Ch. 5: The Shorter Division of Pairs, (Culayamakavagga), p. 392-393, by Ven. Bhikkhu Bodhi


Here is another quote from the same book. This is from the chapter "Notes to sutta MN 43":


  "Vital formations" (ayusankhara), according to MA, denotes vitality itself. They cannot be states of feeling because they are required to keep the body of a bhikkhu alive when he has attained to the cessation of perception and feeling. This special meditative attainment, in which all mental activity ceases, is accessible only to non- returners and arahants who also have mastery over the eight attainments on the side of serenity. For a brief discussion see the Introduction, p. 28, and for the full scholastic account, Vsm XXIII, 16-52. The cessation of perception and feeling will be taken up again in MN 44.
  
  -- Ibid, p. 1237


Lastly, here is a quote from the "Visuddhimagga" explaining the term "Vital Formations":


  
  “‘Vital formations’ are the same as life span; though some say that they are the life span, heat and consciousness. These are the object only of his normal consciousness. There is no death during cessation because dying takes place by means of the final life-continuum [consciousness]. He should attain only after adverting thus, ‘Let sudden death not occur.’ For in the case of sudden death he would not be able to declare final knowledge, advise the bhikkhus, and testify to the Dispensation’s power. And there would be no reaching the highest path in the case of a non-returner” (Vism-mhþ 904).
  
  
  -- Visuddhimagga - The Path of Purification, p. 740, by Ven. Buddhaghosa