If One Bulb Burns Out Will it Affect My Entire String Light?

What happens If one of the bulbs on the string light stops working?

No, they run independent of one another, so if one bulb burns out the others will stay on.  To fix the bulb, you will simply need to replace it like a regular light bulb.

For more information on how to replace string light bulbs read How Do I Replace String Light Bulbs.