This refers to making a motion under Standing Order 163, which states:
If at any sitting of the House, or in a committee of the whole House, any Member moves ‘That the House sit in private’ the Speaker or
the chair shall forthwith put the question ‘That the House sit in
private’, and such question, though opposed, may be decided after the
expiration of the time for opposed business, but such a Motion may be
made no more than once in any sitting:
Provided that the Speaker or
the chairman may, whenever he thinks fit, order the withdrawal of
those other than Members or Officers from any part of the House.
An order under paragraph (1) of this order shall not apply to members of the House of Lords.
According to paragraph 17.22 of Erskine May, if a motion under this standing order is agreed to, then "all the galleries are cleared, including Hansard reporters, with the consequence that there is no report of debates; broadcasting also ceases. The occupant of the Chair may authorise a short suspension to allow these arrangements to be put in place".
Paragraph 6.57 also notes:
Such an order extends to the Press Gallery and requires broadcasting to cease. Following the private sitting in 2001, the sound amplification system has been modified so that it can be used when broadcasting has been turned off.
The majority of uses of this standing order are to engineer an immediate division. Standing Order 41 requires that if fewer than forty MPs take part in a division, the current business under consideration "shall stand over until
the next sitting of the House", and the House moves on to the next business. MPs seeking to derail a poorly-attended private member's bill debate, then, can move that the House sits in private, and hope that fewer than forty members take part in the division. If this is the case, the debate on the private member's bill will be adjourned due to the House being inquorate.