TMT stands for tandem-mass-tag. The idea is to tag different samples with one of the tags then pool all samples together and run them through the mass spectrometer together. Then the reporter groups are split off and quantified (ideally) for each peptide individually. There are different methods with different numbers of isobaric labels. Isobaric means all the labels have the same mass therefore they behave exactly the same in the mass spectrometer at first. E.g. TMT11 means you have 11 different tags with identical masses, so you can pool and process 11 samples at a time.
The protein binding group attaches the label to the peptide. Then the tagged peptides from all samples are run through the chromatography and the spectrometer. At first, the MS instruments simply collects the tagged peptides with different m/z ratios at each point in time for a while. When enough peptides are collected reporter groups are cut off and the peptides then quantified. This cutting-off happens by increasing the internal energy of the collected peptides. Because the cleavage group has the weakest chemical bond it brakes first and releases the reporter group. Again, this step separates the reporter group from the rest. Finally, the cut-off reporter groups are quantified.
The different reporter groups don't have the same mass, otherwise you would not be able to differentiate between them in the MS instrument. But you need same masses before quantification to ensure that the same peptides are all collected together. Therefore, you need to balance out the different masses of the reporter groups. That is the job of the normalization group. So, the normalization group ensures that overall the tags have the same mass and the peptides with different tags are not treated differently in the MS instrument before quantification. Then for quantification the reporter groups (with different masses between each other) are cut off and the MS instrument can therefore detect and quantify them individually. There is a time dependency of the whole process which happens in multiple phases. The whole process makes it possible to compare the amounts of peptides coming from the different samples.
The chemistry in the chromatography column is quite complicated which makes it difficult to compare samples from different experiments. The presence of one peptide might enhance or suppress the signal of another peptide or impact the chromatographic retention time. Therefore, you should only compare within the same sample. More tags TMT11, TMT16 etc. allow you to run more samples in one run.
You can then use one (or more) channels (mass-tags), to tag a standard sample and then compare everything to this standard that is assumed to be identical over multiple experiments. This way you can compare even more samples than available tags. e.g. more than 11.