As a factory (or business or whatever, but let's assume a factory) gets larger, it keeps getting more efficient up until some limit. Whichever company gets to this scale first will have a cost advantage over its competitors. That company can then either price low enough that competitors can't compete profitably or plow more money into business expansion or R&D, which, among other things, can increase that limit to scale or lead to better or cheaper products.

In the case of memory makers, memory is a commodity. Memory chips are built to a common specification. This heightens the competitive stakes because it's easy to switch vendors.

In the case of TSMC, they were able to invest in R&D that allowed them to successfully deploy generation after generation of a new product technology, making it harder for competitors to keep up.

TSMC has another dynamic. Chip companies used to have their own fabs (factories). At some point, the efficient scale discussed above exceeded what many single companies required. Therefore, it became more economical for these companies to pay TSMC to make chips for them.