Care about color temperature because it greatly affects the way you'll look in a lighted vanity mirror or makeup mirror.
We all know how different things can look in daylight versus indoor lighting. The reason is the color of the light coming from light bulbs vs. the color of light from the sun. Needless to say there are many variations of light color. Light color is generally described in degrees Kelvin (K). The color of the light coming from your lighted makeup mirror can greatly affect the way you look.
Until the advent of LEDs, makeup mirrors were illuminated either by incandescent or fluorescent light bulbs.
Incandescent bulbs emit light with a color temperature of approximately 2,700 K which is a comfortable yellowish color that our eyes are quite used to. Anybody who has seen photographs taken with a camera using film (not digital) in incandescent light has observed the yellowish tone they take on. Because we are so accustomed to incandescent lighting, most environments lit by incandescent light bulbs look quite normal to us.
Fluorescent bulbs are usually of the "cool white" variety, emitting light at 4,700 K. Most fluorescents are cool whites because these are the least expensive to manufacture. These have a distinct greenish tinge and the observer of a photograph taken with film has seen the green cast of the photo. "Color corrected" fluorescents are available with color temperatures ranging from about 5,600 K to 6,000 K and cost almost three times as much as cool whites. Quality makeup mirrors that employ fluorescent bulbs use color-corrected fluorescent bulbs.
Incandescent bulbs: 2,700 K.
Fluorescent cool white bulbs: 4,700 K.
Fluorescent color-corrected bulbs: 5,000 K. - 5,600 K.
Blue sky daylight: 5,600 K.
White sky (bright cloud-covered) daylight: 6,000 K.
There are currently LEDs available in a wide range of color temperatures. For makeup-mirrors, the most common temperatures are around 3,500 K, and around 5,500 K. The 3,500 K. LEDs are quite close to incandescent lighting, while the 5,500 K LEDs are close to daylight.
If you have a choice of LED color temperature, consider the situation in which you'll be most often. If you'll be in daylight most often, then select a 5,500 K mirror. Conversely, if indoor lighting is your melieu then select a 3,500 K LED mirror.