Hold On

心為令，氣為旗，腰為纛
The heart commands, vapours are the flag and the waist the banner

肛門不提，丹田氣散，内中空虚，元氣*虧損
When the anus is not pulled up, the vapours around the cinnabar field disperse, the inside becomes empty and one's vitality depletes

A lot of Chinese practices consider the waist to be the most important part of the body, 腰为主宰, the waist dictates. For those practices, the waist refers not only to the anatomical part of the body, but can also point out specific vertebras or extend to the whole part below the navel to the crotch, the pelvic area. Since it is not only the centre of one's body, where the legs and the chest connect, but also the most important place for vitality, most of the organs being more or less located around it, keeping a correct structure in the area is key to a fruitful training. Among the many requirements one stands out, the necessity to literally pull up the anus that you find in a lot of practices (or its symmetrical version, to pull up the bladder) and hang the stomach (or its symmetrical version, to pinch the sacrum vertebras).
For anyone interested by this sometimes overlooked part of the practice, it is important to understand the reasons behind such requirements, connection and insulation, and motion, uprightly pulling up.

Connection and Insulation

The waist is the main connective part of the body, and the place where most of the heating process briefly described in 气 Where is my Bowl of Rice? occurs. Hence, any structural issue in this part will always emphasise on connection and insulation.

Keeping the Fascia Lines Connected

Out of the twelve main fascia lines described in the Yellow Emperor's Internal Canons**, most of the 6 lines starting from the feet extend over the waist, making the angles taken by the buttocks and the stomach crucial for keeping the connectivity of those lines. In other words, an incorrect posture often results in the rupture of those long lines of fascias and basically disconnects the legs from the rest of the body. Pulling up the anus or the bladder and hanging the stomach or pinching the sacrum simply describe one of the motions helpful to maintain a correct posture allowing the connection of the entire body. 

Any angle and change of structure in this particular part of the body will always have the greatest impact on the rest of the body. That is actually why, 提肛吊肚, pulling up the anus and hanging the stomach, and 提膀胱夾尾椎, pulling up the bladder and pinching the sacrum vertebras, though they describe similar angles to be taken, are actually one of the difference between light and grounding skills. Indeed, pulling up first the anus will stress more on the fascia lines on the back of the legs, improving grounding while if the bladder is pulled first, it is the inside of the legs ones that will be stressed, improving lightness.

Insulation

The need for insulation has been already described in External Comes First as far as heat is concerned, but it is necessary, because vapours are also a question of condensation, to understand that such techniques are also a means to counterbalance the negatives effects of the first technique of condensation. Indeed, 氣沉丹田, the vapours submerge the cinnabar field, leads to concentrating vapours as low as possible in the stomach, all the way down to the crotch. If this breathing technique is not made while pulling up the anus or bladder at the same time, it will result in putting too much pressure on the sphincters, which will tend to open. Practically, it may lead to having to go to the toilets more often, which, of course, will not be a good sign. That is why when one is pushing all the way down air while breathing out as it is recommended in a lot of practices, it is very important to simultaneously pull up the anus of the bladder, one move down and one up to balance.

The reasons behind such requirements understood, one shall try to also grasp the motion intended. 

Pulling and Shrinking

Pulling Straight Up

提 means pulling up with one hand, to carry in one's hand with the arm down to be exact, while 吊 means to hang up in this instance. They both include the notion of straightness. Hence expressions like 尾闾中正, the coccyx is straight and centred, to emphasise on such need. One's structure, there, is very important, and if one's pelvic area is not totally vertical, there are lots of chances that the pull will worsen more than anything the situation, leading sometimes to the opposite effect, opening more the sphincters instead of closing them. As mentioned in Methods, it is a question of virtuous or vicious circle, and the straightness of one's pelvic area is the key factor between one or the other, not the pull.

提 is also important because one has to consider the whole motion an arm has to make when lifting up something a bit heavy, and especially the wrist, in order to find which part inside the body can do such thing to pull up the anus or the bladder. 

Finally, if 提 indicates that the part pulling up is upper but very close to the part being pulled, 吊 implies a further distance, so somewhere in the upper body, not around the waist;

Shrinking

Shrinking is the result of stretching the body and pulling it in two opposite directions. Indeed, pulling up the anus has to be linked with another seemingly opposed principle, sitting the hips, or pulling the bladder with dropping the waist.

Hence a right pull up with a right opposed drop should make the stomach retract, the back shrink towards the backbone and the buttocks pull towards each other, hence the saying, 提肛縮腹夾臀, pull up the anus, retract the stomach and pinch the buttocks. 夾尾椎, pinching the sacrum vertebras seems, then, to insist on the importance of this part of the backbone. In other words, if one is pulling correctly his anus or bladder while sitting the hips and dropping the waist, then and automatically, his/her stomach shall shrink and his/her buttocks shall pinch (as well as around the sacrum). If when pulling and dropping none of the above happens, it means that the way the pull is performed is wrong or that one is not pulling with the right part of the body.

This post would seem even clearer if the parts of the body pulling were described. Still, by doing so, the author would go against the old methods, which were about self-discovery, and probably limit the reader to his understanding. Furthermore, the pulling motion has to be modified when one goes from straightness to roundness (see From String to Wood in The Bow, Cornerstone of Elasticity).

*元氣, vitality, also means original vapours, referring then to the inborn vitality while vapours are a general term whether the vitality is inborn or nurtured.

**黃帝內經