It is referring to the Shat Karma of Yoga.
This is referred to in the following verse from the same text:
Karma shatkamidam ghopyam ghataśodhanakārakam
Vichitraghunasandhāya pūjyate yoghipungavaih ||
These six kinds of actions which cleanse the body should be kept secret. They produce extraordinary attributes and are performed with
earnestness by the best of Yogîs
and mentioned in the following:
Dhautirbastistathā netistrātakam naulikam tathā
Kapālabhātiśchaitāni shatkarmāni prachakshate ||
The six kinds of duties are: Dhauti, Basti, Neti, Trâtaka, Nauti and
Kapâla Bhâti. These are called the six actions
A strip of cloth, about inches wide and 5 cubits long, is pushed in
(swallowed), when moist with warm water, through the passage shown by
the guru, and is taken out again. This is called Dhauti Karma
Squatting in naveldeep water, and introducing a six inches long,
smooth piece of ½ an inch diameter pipe, open at both ends, half
inside the anus; it (anus) should he drawn up (contracted) and then
expelled. This washing is called the Basti Karma
A cord made of threads and about six inches long, should be passed
through the passage of the nose and the end taken out in the mouth.
This is called by adepts the Neti Karma
Being calm, one should gaze steadily at a small mark, till eyes are
filled with tears. This is called Trataka by âchâryas.
Sitting on the toes with heels raised above the ground, and the palms
resting on the ground, and in this bent posture the belly is moved
forcibly from left to right just, as in vomiting. This is called by
adepts the Nauli Karma
When inhalation and exhalation are performed very quickly, like a pair
of bellows of a blacksmith, it dries up all the disorders from the
excess of phlegm, and is known as Kapâla Bhâti.
Benefits obtained by performance of each of these actions are also mentioned in the text. Like for Trataka following are the benefits:
Mochanam netraroghānām tandādrīnām kapātakam Yatnatastrātakam ghopyam
yathā hātakapetakam ||
Trâtaka destroys the eye diseases and removes sloth, etc. It should be
kept secret very carefully, like a box of jewellery
Some of these practices should be performed under someone's guidance. For example, the first two. Trataka can be done on one's own. Swami Vivekananada also recommends the technique.
Note: If you are looking for pictorial descriptions of these 6 Karmas, then Swami Ramdev's book "Yog Rahasya & Chikitsa" will be helpful.
How to confirm that whether impurities exist in the Nâdis or not?
I am not sure why the introduction is talking about Nadi impurities with respect to Shat Karma, but the text actually suggests that a person who is obese (fat) should undergo these 6 actions. For others it is not necessary to do so.
If there be excess of fat or phlegm in the body, the six kinds of
kriyâs (duties) should be performed first. But others, not suffering
from the excess of these, should not perform them.
Because excessive fat in the body is a hindrance for someone to master several of the Yogic postures. And, without mastering them the Yogi can not become adept in Hatha Yoga which in turn is the prerequisite for mastering Raja Yoga.