How can she hold the link to all humans?

There are many theories about the answer to this question. However, the most popular theory involves probability and some luck. It is speculated that by pure chance, our female ancestor's DNA had the capability of resisting genetic change. So, this DNA was passed on as the dominant code from generation to generation. Hence, Eve’s mitochondrial DNA was passed on to her daughter who then passed  it on to her children and so on. By some chance, the environment, and situations in Mitochondrial Eve’s time played to the benefit of her DNA and it was able to be transmitted from her tribe and so on to other tribes until the DNA infiltrated the rest of the population.
The theory revolves around the idea that mitochondrial DNA (mDNA) is inherited directly verbatim from a maternal carrier. In mitochondrial DNA, there is no chance of genetic variation except for those that occur through mutations during copying. As time went on, however, it is evident that Eve’s mitochondrial DNA underwent mutation and change.  Therefore, these mutations fed into and formed different variations of the initial creator set of DNA.
However, it should be noticed that mutations most often occur in the control region(500 bases) of the mDNA. This is because this region doesn’t have a specific function and is neutral. Mutations that occur on other parts of the mDNA are often eliminated when passed on to the next generation. Only the mDNA with mutations in the control region survive. As a result, if mutations in the control region of the mDNA are traced back through generations, we will eventually find one single set of “creator” mitochondrial DNA for all Homo Sapiens.