She thought it might calm him down. She thought it might help him work out his problems. He privately thought it was a ridiculous idea, one of the worst he had heard since the time Sirius and James decided that it would be funny to release every bludger in the Quidditch equipment room and Remus hadn't been able to convince them otherwise. However he also privately thought that at that point, he'd be willing to try anything that might possibly make things more comfortable.
Since that slimy git Severus Snape had run off back to the Death Eaters after murdering the Headmaster, Remus didn't have anyone to make the Wolfsbane potion unless he travelled all the way to St. Mungo's every single month. And since they weren't staying in Grimmauld Place anymore, it was quite a distance. Of course, he could apparate—he was a wizard after all—but he chose not to.
Tonks thought he wanted to make himself suffer. It had been almost a year after all. They both knew he still felt guilty for letting his best friend go to the Ministry, recklessly as ever; he wasn't in denial about it or anything. Remus and Tonks both knew that Remus was supposed to be the rational one, the one who stopped Sirius from doing stupid things, and that this time he'd tried, but it had been half-hearted. Remus was the only one who could ever get Sirius to stop being a bloody idiot, and if he had tried harder, maybe Sirius would have listened.
How Tonks thought that all of this could be cured by meditation, Remus didn't know, but he promised her that he would at least make an effort. He sat on the floor with his legs crossed as she directed, and when the change came, he turned into a werewolf and scratched up the furniture and felt incredible pain and everything was the same as it always was, despite the effort.
"You have to get used to it first," Tonks said the next day. She ran a hand through her hair, currently bright orange, and said, "You have to do it every day so that you can be really relaxed when the full moon comes." So he tried meditating again and he thought about how ridiculous it was and how he could be doing something productive, realizing of course that he wasn't clearing his mind like Tonks had told him to, but it was just meditation, not Occlumency or anything so he was fine with pretending.
"How are you feeling?" Tonks asked him, smiling to see him sitting on the floor with his eyes closed and his hands on his knees. Remus lied and told her that he was feeling excellent, much more relaxed. He didn't lie and tell her that he spent the whole hour thinking about Sirius dying and Dumbledore dying and the burden that Harry had that Remus couldn't do anything about and being with Tonks and... everything, all while Tonks was sitting serenely next to him and believing that he was calmer already.
He looked over at her, and watching her breath slowly made him feel a bit more relaxed, but as she couldn't really be sitting next to him while he made his transformations every month, he figured he ought to work a little harder.
He closed his eyes again and immediately thought about Sirius. And then Tonks. And then Sirius again. Then Dumbledore, Harry, Snape, Sirius again. None of which helped him relax.
So much for meditation.