"Filling someone's shoes" means doing the job that they used to do. You use this expression when the first person did a good job. 

If that person was really good at their job, you might say that you "have some big shoes to fill". It means that it's going to be hard for you to do the job as well as they did it.

When you take over a job from someone else, it's polite for you to say that you "have some big shoes to fill".