What does it mean to "admonish one another?"
The word "admonish" is defined in our English dictionary as "to reprove gently but earnestly;" "to counsel (another) against something to be avoided; caution;" "To remind of something forgotten or disregarded, as an obligation or a responsibility" (The American Heritage Dictionary).
The Greek word for "admonish" is noutheteo, which is where we get the English word nouthetic. It means, "to impart understanding, to set right, to lay on the heart" (Kittel).
"The stress is on influencing not merely the intellect but the will and disposition” (Kittel). “It means to warn people of the consequences of their behavior” (MacArthur). It refers not merely to academic data imparted impersonally but to instruction for the purpose of correcting and changing people. It is teaching with an element of warning, designed to direct the sheep to holy living” (John MacArthur, 1 & 2 Thessalonians, p.170). 1 Corinthians 4:14 gives us an illustration of this when Paul says to the Corinthians: “I do not write these things to shame you, but as my beloved children I warn you.”
So if we could compare admonishing to teaching we would say that “teaching is the impartation of positive truth. Admonishing is the negative side of teaching” (John MacArthur).