You may hear this in two different contexts.
1-Indemnity is another word for insurance. It means that the insurance company will cover/help cover costs incurred by a policyholder if they are sued or have a loss. You may see this word in your policy documents when outlining what is covered or if you experience a claim you will receive correspondence from insurers saying that ‘Indemnity is agreed’ or ‘indemnity is declined’
2-Your landlord may ask you for an Indemnity Letter, this is very common. In simple terms if you indemnify your landlord, you are promising that if someone tries to claim from you, that you won’t also try to bring your landlord in on it. You keep your risks separate even when sharing a mutual space. Your landlord is ‘Held Harmless’ in events that occur within your business.