To have the conscience seared means to have it made insensitive, like flesh cauterized by a hot iron. The passage may also suggest being branded as a mark of hypocrisy and guilt.
Definition
To sear means to make insensitive as though by burning with a hot iron. In the relevant passage, it may also mean to brand, suggesting a conscience marked by hypocrisy and guilt.
Biblical Usage
First Timothy 4:2 speaks of people whose consciences are seared or branded. The image describes an inward moral insensibility, compared with the loss of feeling in the surface of a deep burn after healing.
Historical Background
The Greek verb can mean “burn with a hot iron,” reflected in the King James Version, or “brand,” reflected in the Revised Version. Branding criminals was understood as marking their infamy for all to see.
Historical Bible Dictionaries
International Standard Bible Encyclopedia (ISBE)
<p>ser: In 1Ti 4:2 for (kausteriazo), "burn with a hot iron" (compare "cauterize"), the King James Version "having their conscience seared with a hot iron," and the Revised Version margin. "Seared" in this connection means "made insensible," like the surface of a deep burn after healing. The verb, however, probably means "brand" (so the Revised Version (British and American)). "Criminals are branded on their forehead, so that all men may know their infamy. The consciences of certain men are branded just as truly, so that there is an inward consciousness of hypocrisy." See the commentaries</p>