This is the 8878th most frequent Russian word.
принимающая
"Accepting" or "receiving."
The word 'принимающая' here acts as an adjective describing the party (сторона) that is hosting or receiving others.
Принимающая сторона заботится о гостях.
The host party takes care of the guests.
In this sentence, 'принимающая' also functions as an adjective qualifying the family as the one hosting or receiving guests, exchange students in this case.
Эта семья является принимающей для студентов по обмену.
This family is the host for exchange students.
Here, 'принимающая' describes the company that is hosting or accommodating someone or providing services in a hosting capacity.