What is the word for bright colors such as green?

If you are talking about the softer hues of pink, yellow, and green, those would be pastels:

From Wikipedia:

Pastels or pastel colors are the family of colors which, when described in the HSV color space, have high value and low to intermediate saturation. The colors of this family are usually described as "soothing", "soft", "near neutral", "milky", "washed out", "desaturated", lacking strong chromatic content.

Pink, mauve, and baby blue are typical pastel colors.

However, since you mentioned "bright" colors, I suspect you are referring to neons:

Does this help? Sample information given here. Please read the whole article about types of colors in the link I gave you.

Warm Colors

Warm colors are made with red, orange, yellow, or some combination of these. Warm colors tend to make you think of sunlight and warmth.

Cool Colors

Cool colors are made with blue, green, purple, or some combination of these. Cool colors might make you think of cool and peaceful things, like winter skies and still ponds.

Did you mean vivid colors? These are extremely bright, flashy colors.