The members of the executive branch are drawn from the leadership of parliament (the legislative branch).
In a parliamentary system, the main executive branch office is that of the prime minister. The prime minister is the leader of whichever party receives the greatest number of seats in parliament when elections are held. So there is a direct connection between parliamentary power and executive power.
As far as how cabinet members are appointed, that varies within parliamentary systems. In the British system, cabinet members are appointed from sitting members of parliament. In some other systems (such as Switzerland or Belgium), cabinet members must then give up their posts in parliament so that there is a bit more separation between the legislative and executive branches of government.