Your mother is so fat, she solves the Travelling Salesman problem...

Your mother is so fat, she solves the Travelling Salesman problem in O(1) by visiting all cities simultaneously.
This is a programming joke and also a "your mother" joke. "Your mother" jokes are a type of joke that is used as a put down in some parts of american culture. The jokester makes an insult directed at the listener's mother, which is supposed to insult her and by association the listener. These jokes usually insult the mothers weight, but they can also insult her intelligence, or other attributes.

To understand this joke the listener has to understand the Travelling Salesman problem, as well as O (Big O) notation.

The Travelling Salesman problem is probably the seminal example of a NP Complete problem - which is a class of problems that computers have a hard time solving efficiently. The problem is fairly simple: given a collection of cities, visit all of them with the shortest amount of travel.

O notation is a way of showing how many operations a computer has to perform in order to solve a problem, and the fastest amount of time is O(1). That means that the computer could get it done in a single clock cycle (which is less than a second).

So, this joke is saying that the size of your mother allows her to break a notoriously hard problem (which many software engineers and computer scientists believe to be impossible to solve in a short amount of time) by being in all of the cities at the same time.

Or, to break it down more: your mother is really fat.