Redundancy, usually flagged by an editor with the letter R, is the use of the same word or phrase over and over within a piece of writing.
This is a problem that can easily be fixed with a little creativity. Typically, in any good piece of writing, you really want to avoid using the same word or phrase, especially within the same paragraph. This is especially true when paragraphs are short - less than half a page long. There should be little to no repetition of words, i.e. "cats" in the same paragraph. This can be changed or avoided in one of two ways: by changing the redundant word to something with the same meaning, or by rewriting the sentence so it says the same thing, but in another way. I'll give you an example below; the first paragraph uses a redundant word that need editing, and the following two offer different ways of rewriting it to make it a stronger piece of work.
Cats are cute. My cat is very affectionate and has a typical cat name; Fluffy. Cats can climb trees, which is an important skill for a cat to have, especially when being chased by a dog.
Cats are cute. My feline is very affectionate and has a typical pet name; Fluffy. She can climb trees, which is an important skill for her to have, especially when being chased by a dog.
Cats are cute and can climb trees, which is an important skill for them to have, especially when being chased by a dog. My feline, Fluffy, has a typical name and is very affectionate.
So you see, in the first example, the word "cat" is very over-used. It appears far too many times, and makes the writing seem elementary, or less sophisticated. In the second example, the paragraph remains the same, but with a little help from some useful synonyms, the writing sample becomes less tedious/boring for the reader. A little bit of variation keeps them on their toes, and helps to prevent them from skimming. The third variation completely changes the wording, but keeps the intent of the story intact.