The LOGIC ecigs are a two-part e-cigarette. What you have is the battery, the long part. This is part that you can recharge and the end lights up blue.
Not to be confused with the BLU brand, though. Some eCigarettes light up green at the end and others light up red, to mimic a real cigarette.
I like the blue end because when you’re using them in a smoke-free environment, it’s obvious that you’re not smoking a real cigarette.