My daughter has been in nursery since she was 9 months. She'll be 2 next month. I don't think at that age they do much 'formal' learning, but they do learn lots through play and interaction. It's hard to know exactly what she gets from being there and what she gets from being home with us (she's in nursery 4 full days a week). But she brings home lots of art. They do outdoor activities, like playing in the mud kitchen and going on walks. They do lots of messy play, which I don't do at home because I hate cleaning up after it. She's really good about putting her shoes and coat on and off when we go out/come in the house. She's also really helpful, helps me clean up, put things away, etc. I'm not sure that's just from nursery, but certainly it reinforces it. She knows so many words and speaks in sentences. She can also count a bit, though doesn't always get the order right! She also knows some colours. Again, really not sure that's all down to nursery, as we count and learn about colours and do lots of reading and talking at home, but certainly doesn't hurt.
She's also gotten much better about sleeping anywhere since she's been at nursery (it's a Montessori type set up with just cushions and floor beds around the edges of the room so she naps there or outside on a blanket in the grass in the summer). She's much better with brushing her teeth lately as well as they've been doing a lot about teeth and talking about dental care with the kids. I think probably a lot of that goes over her head because she's little still, but it goes up to age 5 so it's mostly for the older kids (they're altogether in one class). But definitely she's better with her teeth and asks to brush them and does it much better on her own lately.
It's also been amazing for her socially. We live in a rural area. There are some baby groups, but not much for toddlers, certainly not that isn't a bit of a drive away. So there's only so much we can go to in terms of groups and classes. But it's been wonderful for her to make friends at nursery. She talks constantly about her friends and the teachers. Every time we drive past (nursery is just down the road from our house), she starts naming all her friends there from the back seat (Sarah! Lily! Emily!). When we had her over Christmas (they're closed for 2 weeks), she kept asking to watch videos on my laptop from the Christmas play so she could see her friends and would point to everyone in the play and name them. Many mornings when she goes in, she gives all her friends a hug when she sees then. It's really sweet!
For us, I think it's been wonderfully beneficial. I think if you can be home and you enjoy it and you can arrange social and other activities on a daily basis, then great, there's no reason you have to put your child in nursery. If you need to work or you feel you can't find the time and energy to plan activities, do classes, go to groups, find lots of opportunities for exploration and play, then I think nursery is great. Of course, a lot of it comes down to the quality of the nursery you find and whether their approach is a good fit for your parenting style. We've been really lucky to find somewhere that was such a good match for us.
But yes, I think it's been such a benefit, and even if I didn't have to work (I do), I think personally I would still opt to have her in nursery a couple days a week just for the experience. I'm just not into all the groups and classes and shuttling around to different activities all day and I think that's really important to have that social development. The only problem really is that it's expensive! And that cost can just be so prohibitive, even if it's something you really do feel like is the right choice for you.