Impaired means to be in an imperfect or weakened state or condition: as diminished in function or ability : lacking full functional or structural integrity.  You can be hearing impaired, visually impaired, or have impaired movement.  It also means to be intoxicated. 

The word "impaired" originates from the Old French "empeirer," meaning "to make worse."  This, in turn, comes from the Late Latin "pejorare," also meaning "to make worse," which is related to the Latin word "pejor," meaning "worse". Ultimately, the root traces back to the Latin word "pejor," meaning "worse," or potentially from "ped-yos-, referring to "foot" or "stumbling".

The verb "impair" itself is recorded earlier, from the Middle English period (1150-1500), with the OED's earliest evidence from 1340.  
According to the Oxford English Dictionary (OED), the earliest recorded use of the adjective "impaired" is in 1559, in a translation by Peter Morwyng.  
The term "hearing-impaired" was first used in the 1940s, specifically 1946.  

Examples of "impaired" used in a sentence:  
"In your former life you were an educator who taught math to language-impaired kids."
"She faces charges of driving while impaired, careless driving, and speeding." 
"The children were so impaired that a third of them had to be home-schooled." 
"The impaired woman's 11-year-old daughter was with her in the car when the crash occurred."  
"The man's speech is slightly impaired due to a cleft palate." 
"The patient has impaired mobility after having a stroke."

I've been doing some "impaired" writing lately.  (Sigh ...) Sadly, that probably means some heavy editing is in my future! *

*This just in ... Ron meant to write impaired-writing and not ""impaired"" writing". One of those things is not like the other. 

@Bill W's etymology of impaired shows another example of how in English a word can change from a verb to an adjective. Its root in Late Latin is a verb and it is still a verb in its journey through Old French. As @Bill W points out it is a verb in 14th Century English (impaired being past tense of impair) but by the 16th Century impaired is also an adjective.

I love that we can look back and see how English has evolved. It reminds us that as a living language English continues to evolve. Whether that is for better or worse is often the basis of heated argument.

@Paladin Oh, those etymologists would have us empare the word impair and replace it, they being all conjunctive and such. Well, the damage is done!