A tautology is an expression or phrase that says the same thing twice, just in a different way. For this reason, a tautology is usually undesirable, as it can make you sound wordier than you need to be, and make you appear foolish. Occasionally, a tautology can help to add emphasis or clarity, or introduce intentional ambiguity, but in most cases it's best to choose just one way to state your meaning and eliminate the extra verbiage.
Sometimes a tautology involves just a few words that mean the same thing. Consider the following sentence:
I went to see him personally.
This is an example of tautology, because the adverb "personally" repeats the idea already expressed in the single word "I". In everyday conversation, the addition of "personally" is used for emphasis to point out that the subject of the sentence is invested in the action, has overseen something, etc. Technically, the word "personally" doesn't add any new information and could be cut from the sentence without changing its meaning.
In the realm of logic, a tautology is something that is true in all circumstances. A common example of a logical tautology is the following:
The dog is either brown, or the dog is not brown.
This sentence is always true because one or the other must be so. This is different than a statement that says, "The dog is either brown, or the dog is white," because dogs can be black, gray, or a mix of colors. Note that when you put both halves of the logical tautology together, it feels a bit redundant, just like a verbal tautology.