Correct spelling


Correct spelling, explanation: improvement comes from the verb improve and a noun-creating suffix -ment. In fact, not much happens here besides rather standard suffixation as it’s a word created in a very regular manner.

Definition of improvement:
1. a correction, an act of making something better
I have to admit that since I started paying attention to my diet I’ve seen a huge improvement in my health.
Our boss said that he thinks there is still room for improvement here.

Incorrect spelling


Incorrect spelling, explanation: this spelling of improvement can most likely be caused by the pronunciation of the word and the fact that the e in improve is silent. Improvment is, however, an incorrect word, as the base word does have the e and it can’t be deleted when adding a suffix. English aims to have a balance between the number of consonants and vowels in a word, so getting rid of a vowel here would be unnatural.