An achromatic lens is actually a combination of two lenses. The light enters through a convex lens, and then passes through a concave lens. The two lenses are also made of materials with two different refractive indexes. This is assembled in such a way as to minimize chromatic aberration.
The reason behind this is that a normal lens will not bring the focus point of light consisting of different wavelengths into exactly the same point. The focal length depends on refraction and index of refraction of the material used to make the lens. Lenses consisting of a single element, and having a single refractive index, could bring only a specific wavelength of color to a specific focus point.
Having a combination of lenses with two distinct refractive indexes, otherwise known as a doublet for chromatic aberration, means that light of two specific wavelength can be brought to a given focus point. The amount of chromatic aberration depends on the dispersion of the glass.
The use of a strong lens made from a low dispersion glass like crown glass coupled with a weaker, high dispersion glass like flint glass can correct the chromatic aberration for two colors. Using materials with specific refractive indexes it is possible to bring the focus points of two specific wavelengths of light to a single specified point in space.

Partial credit to m_turner and

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