To determine which type of meteorites are compositionally and texturally similar to terrestrial basalts, let's first understand the characteristics of each option provided:

1. Iron Meteorites: These meteorites are primarily composed of iron-nickel alloys. They are not similar to terrestrial basalts, which are silicate-rich rocks, because iron meteorites have a metallic composition that is quite different from basalt's mineral composition.
2. Carbonaceous Chondrites: These are a class of chondritic meteorites that contain high percentages of water and organic compounds. They are among the most primitive meteorites and do not have the same texture or composition as basalts, which are rich in pyroxenes and plagioclase minerals.
3. Enstatite Chondrites: These meteorites are primarily composed of the mineral enstatite. While they are silicate meteorites, their mineralogy does not match the pyroxene-plagioclase combination typical of basalts. Therefore, they are not compositionally similar to terrestrial basalts.
4. Achondrites: These meteorites have a composition and texture that closely resemble terrestrial igneous rocks, such as basalts. Achondrites are stony meteorites that have, like basalts, undergone processes such as melting and differentiation. This similarity makes them the correct answer when looking for meteorites that resemble terrestrial basalts.

Based on the above understanding, Achondrites are the meteorites that are compositionally and texturally similar to terrestrial basalts. They share similar mineral compositions and textures due to similar geological processes such as partial melting and crystal differentiation.

The correct answer is therefore Achondrites.