A polite form of 'yukkuri' meaning 'slowly' or 'at one's leisure'; often used to invite someone to take their time (common in customer service).
どうぞごゆっくりお召し上がりください。
Please enjoy your meal at your leisure.
ごゆっくり休んでから出発してください。
Please rest well before you leave.
店員が『ごゆっくりご覧ください』と言った。
The shop clerk said, 'Please take your time looking around.'