In your example, "way" doesn't change the meaning of the sentence, but it adds emphasis to "too fast."
This use of "way" is very common in spoken English. (In fact, it's way too common!)
It's not a good idea to use it in writing, unless it's quoting a person saying it.
But in everyday speech, it can add emphasis to a lot of things.
Notice how each example here adds emphasis: "It's hot" -> "It's too hot" -> "It's way too hot!"
Normally, "way" gives emphasis to the word "too," but in modern slang, people add it to many words.
("That movie was way cool!" "That haircut is way cute!" "That book is way boring!")
These examples are not grammatically correct, but people often use them in speech.