Elastic modulus may be considered in uniaxial tension, where the higher the modulus the more pressure is required to extend the sample by a certain distance than for a different material with a lower modulus, all gemoetrical parameters being the same e.g. steels may have a modulus of ~210 GPa & Aluminium alloys ~70 GPa.
The same is true in compression, where a high modulus means that a material is more resistant to compression than another with a low modulus, all geometrical paramaters being the same.
A material may be stronger in compression than tension, as strength is independent of modulus, although high modulus materials are often strong.