The world number two, the top seed at Queen's, opted out of Roland Garros with a back injury but returned in west London and won twice in one day to set up a match against Ben Becker for a place in the semi-finals.
Murray, the reigning US Open champion, was delighted to return to action having missed the French Open and is looking forward to the remainder of the tournament at Queen's.
"I think it can be easy to take things for granted sometimes," he said after his 6-2 6-2 win over Marinko Matosevic this afternoon.
"I played pretty much every Slam for about seven years and I missed it. It was difficult watching and not being there.
"You realise how much you love competing, and you love being around the tournaments when everything is good and you're healthy and you're playing every week.
"You don't often think about it that much, and when you're away from it and you miss one of the biggest tournaments, one of the tournaments you prepare extremely hard for and put the hard work in for, then it's tough.
"I was really looking forward to getting back on the court again, and hopefully I can have a good week."
Murray saw off Matosevic after completing his second-round match against Nicolas Mahut earlier in the day.
Rain on Wednesday meant his meeting with Mahut, who had beaten Murray at Queen's 12 months ago, had been postponed until Thursday, with the Scot already a set up.
The Wimbledon finalist went on to complete a 6-3 7-6(7/4) win over the Frenchman and was pleased to have come through two matches in one day.
"I feel good," he added. "You know, that was what was most pleasing about yesterday was a lot of stops, starts, having to warm up and cool down and stuff. Everything felt good, and I woke up this morning with no real stiffness, which is good."
Murray will now face Becker, who beat seventh seed Alexandr Dolgopolov in the third round, on Friday with a potential semi-final against Jo-Wilfried Tsonga in the offing.