Krenath was a term within the Vulcan language which had an entirely different and misunderstood meaning to Humans. It was typically used in regards to an illegitimate child that was born out of marriage which meant inhabitants of Earth believed the word to mean "bastard" or as "shamed one". However, this was not the case as Vulcan society had a heavy emphasis and importance on family kinships. As such, children born out of marriage were considered a wronged party and that the mistake lay on their elders. This meant that a krenath was afforded every possible redress which included fully status in both families with the parents themselves being stigmatized.
In 2270, Spock learnt that he had mated with Zarabeth on the planet Sarpeidon's past which resulted in him possessing a son in the form of Zar. This led to him using the Guardian of Forever on Gateway to bring his son into the 23rd century where he attempted to teach him of his Vulcan heritage. During this time, Zar came to believe that his fathers descent into emotion on Sarpeidon's past was actually due to the effects of time travel and that he did not love his mother. This combined with Spock's seemingly harsh teachings led to Zar believing that his father saw him as a Krenath and that he was a disgrace. However, Spock later informed him the true meaning of the word and that he was willing to accept a serious breach in Vulcan custom in order to bring Zar into his family. This revelation completely changed Zar's opinion of his father and was greatly moved by the act. (TOS - The Yesterday Saga novel: Yesterday's Son)