Several verses give this general teaching:
Genesis 2:24 Therefore shall a man leave his father and his mother, and shall cleave unto his wife: and they shall be one flesh.
Matthew 19:5 And said, For this cause shall a man leave father and mother, and shall cleave to his wife: and they twain shall be one flesh?
Matthew 19:6 Wherefore they are no more twain, but one flesh. What therefore God hath joined together, let not man put asunder.
Mark 10:8 And they twain shall be one flesh: so then they are no more twain, but one flesh.
1 Corinthians 6:16 What? know ye not that he which is joined to an harlot is one body? for two, saith he, shall be one flesh.
Ephesians 5:31 For this cause shall a man leave his father and mother, and shall be joined unto his wife, and they two shall be one flesh.
First phrase: When a man and a woman get married, they are to form a separate family unit. The man is to leave his father and mother and be joined to his wife. A new family is to be formed that is distinct from either of the families the two came from. By the way, the man is not told to join to his wife's family but to join his wife. I do not think this verse teaches against ever having living arrangements in the same house. This is much more common in some cultures than in others. Many times, it is a financial necessity. However, some form of separation must be made and a separate place to live is probably the best arrangement. When the in-laws are too much a part of the new marriage, they often weaken the new family and the new relationship that is to form.
Second phrase: These two, husband and wife, become one flesh. 1 Corinthians 6:16 teaches us that adultery breaks this union of one flesh. Therefore, the Bible is referring to the physical union of husband and wife in marriage. Neither the wife or the husband is to have full mastery over their own bodies because they are now one. 1 Corinthians 7:4 states, "The wife hath not power of her own body, but the husband: and likewise also the husband hath not power of his own body, but the wife." They are no longer simply two different people with two different bodies. They belong to each other in a very literal way.