Lautering usually consists of three steps: mashout, recirculation, and sparging.
The purpose is to stop all of the enzyme action and remove sugars that may be trapped within the grain following the mash. The reason for doing this is to get the biggest "bang for your buck".
Lautering is simply the process of using the grain bed as a filter medium to drain and rinse the sweet wort through as it moves to the next step of the brewing process, the boil.
Mashout is the term for raising the temperature of the mash to 170°F (76°C - 77°C) prior to lautering. This step stops all of the enzyme action (preserving your fermentable sugar and protein profile) and makes the grain bed and wort more fluid.
Inactivation of enzymes active in mashing
This is the classic function of the mash out : to make inactive the enzymes that work in the mashing (mainly the beta-amylase, since the alpha-amylase can continue to have a certain activity).
To achieve this, the temperature at the end of the mash should reach 76°C / 77°C and rest around 10 minutes in this temperature. Exceeding this temperature will end up extracting tannins of the wort generating astringency.
Decreased wort viscosity
The other objective of the mash out is to reduce the viscosity of the wort , facilitating the extraction of sugars, making the wort recirculation and washing more efficient.
Case the mash-out is skpipped the recirculation will be started right after the mashing.
During the wort recirculation time (20 to 40 minutes) its temperature will naturally drop. Assuming the mashing was finished at 65°C, it will drop to 60°C easily.
Suppose the beer profile would be with more body. If beta-amylase continues working without control, it will consume a lot of sugars and there will be no residual sugar left to fill up the beer . Some other enzymes (like protease) also acts at this range of temperature (although with low activity, since its optimum range is around 50 degrees). This means that it can still break down some medium molecular weight proteins that would also give body to beer.
Conclusion: If the Mash-out is not done, the enzymes will continue working and you would lose control over the sugar and protein profile of the wort.
It is recommended that do not skip the mash out phase , because this suppression reduces the efficiency of mashing and makes you lose control over the recipe.
Recirculation is a simple step (during or after the mash out) that will remove unwanted solid particles and proteins of the brewing wort. Making a proper filter bed (through the mash grains) in your mash, will bring a really big improvement in the clarity and quality of your beer. The reduction in haze-inducing proteins alone will make a huge difference in the appearance of your beer.
In case of BIAB, just suspend the bag and puor the wort on the bag. It will filter the solid particles.
In case of other method, avoid stirring the wort in order to keep the particles seated in the bottom of the vessel.
The idea is to recirculate once or twice the volume of the wort.
Mashing out and Recirculation (together)
The recirculation normally should be done after the mash out, but it can be done together the mash out. Keep the wort temperature the same, around 170°F (76°C - 77°C) and recirculate the wort. Some time is earned in this case.
It is a bit more compliclated because the heating must be controlled and recirculation must be done at the same time.
Sparging is the function of rinsing your mash grains with hot water, same temperature of mash out and recirculation - around 170°F (76°C - 77°C) - to maximize the amount of sugar still available in the grains from the mash process, without extracting tannins.
The sparging must be done right after the recirculation (never before).
In the case of BIAB just start puoring the hot water on the bag.
In case of othe rmethods, the wort must be previously transferred to another vessel/container and the grains must be rinsed/washed with new clean hot water.
In order to avoid extract the tannins, the desirable water pH should be below 7,0, ideal would be below 6,0 (but not below 5,5).