The noun "omission" comes from Latin, derived from the verb omitto ("to let go, disregard").  It entered English via Old French (omission) (in the form of the Anglo-French omissioun), into Middle English (omissioun) in the mid-14th century. The Latin omissio is an action noun formed from the past participle stem of omitto, literally meaning "a letting fall". 

According to the Oxford English Dictionary (OED), the noun omission was first used in English around 1400 during the Middle English period (1150-1500), appearing in works such as Rolle's Form of Living. 

Examples of "omission" used in a sentence:
"it was an omission on our part" 
"He has lied large and small, directly and by omission." 
"There are a few omissions in the list." 
"The police officer was reprimanded for the omission of his duty to inform the suspect of his rights."
"Her omission from the team was surprising." 

Don't confuse omission (leaving something out or excluding something) with emission (the production and discharge of something, especially gas or radiation).  

Just the facts:

OMISSION Definition & Meaning - Merriam-Webster

OMISSION Synonyms: 36 Similar and Opposite Words | Merriam-Webster Thesaurus