Please explain the phrase, "thou shalt be saved, and thy house".

You did not give a scripture reference. I can only guess that you are referring to the Philippian jailer and his household.

Acts 16:30-31 [30] And brought them out, and said, Sirs, what must I do to be saved? [31] And they said, Believe on the Lord Jesus Christ, and thou shalt be saved, and thy house.
See All... And brought them out, and said, Sirs, what must I do to be saved? And they said, Believe on the Lord Jesus Christ, and thou shalt be saved, and thy house.

Again, to some degree I will guess as to your problem with this passage. It may be that a brief glance at the passage could lead someone to think that the jailer believed and his family was automatically saved. Of course, this would go against many other passages that deal with the personal nature of salvation. So we must look further.

Certainly, Paul was aggressive in reaching entire families for the Lord. He did not look on this opportunity as a chance to see one man saved. He immediately aimed to see the entire household saved. We should remember that in our witnessing today.

However, were the family members and servants saved because the jailer got saved? Certainly not! If we read a bit further in the text, we will see what happened.

Acts 16:32And they spake unto him the word of the Lord, and to all that were in his house.
See All... And they spake unto him the word of the Lord, and to all that were in his house.

First of all, we see that Paul and Silas did not just give the word of the Lord to the jailer. They also gave it to all that were in his house. They took his receptiveness as an opportunity to witness to the entire family. Now notice as the story continues.

Acts 16:33And he took them the same hour of the night, and washed their stripes; and was baptized, he and all his, straightway.
See All... And he took them the same hour of the night, and washed their stripes; and was baptized, he and all his, straightway. 34 And when he had brought them into his house, he set meat before them, and rejoiced, believing in God with all his house.

After the entire family received the witness of Paul and Silas, they were all baptized. Then, after feeding the former prisoners, the jailer "rejoiced, believing in God with all his house." Verse 34 plainly states that "all his house" believed. No one got saved or baptized because papa got saved. They all got saved because they themselves heard the word and believed.

They all heard the word of the Lord. They all believed. They were all baptized. They all rejoiced. What a wonderful testimony of the working of God in the salvation of this family!