welcome home; welcome back
A fixed polite greeting said to someone who has just returned home. Often shortened to おかえり in casual speech.
「ただいま」「お帰りなさい」
"I'm home!" "Welcome home."
お帰りなさい、旅行は
Welcome back! How was your trip?
おかえり is the casual shortening of お帰りなさい, used among family and close friends rather than in polite or formal contexts.
From the honorific prefix お + the 連用形 (continuative form) of 帰る (to return) + the polite imperative なさい (from なさる). Literally 'please return', now a fixed greeting.