A tattoo isn't complete and fully set until the healing process is finished. Each tattoo artist will have a set of aftercare instructions, and it's important that you follow them to the letter to prevent infection. You have carved into your flesh, which exposes you to bacteria. There are some variations in care advice, but it generally consists of repeated daily washing and drying and application of a moisturizer. Under no circumstances should you allow your tattoo to be covered with plastic wrap during the bandage phase. Yes, people can see it without exposing it, but it can create a bacterial breeding ground.