Listen to them talk. Ask them questions about their lives (past and present) and listen to them talk, do the whole "active listening" skills thing. This means the most to many of them.
I base this advice off of my experience working in memory care, I was a caregiver in a memory care nursing home for about a year (memory care nursing homes are specifically for residents with various severity levels and types of dementia).
Practical things are of course always great, but it's the social/emotional care that means the most to people who are on the cusp of death (to put it bluntly), which includes elderly widows (nursing homes are full of them, as women tend to live longer than men).
Also, with permission, appropriate physical affection is huge (hugs, holding their hand, firm but gentle shoulder squeeze or pat on the back for encouragement, etc).
Even without severe dementia, something I observed in every resident I ever cared for, both memory care and regular during my clinical training, was the phenomena of how the full earthly life cycle tends to come full circle, mentally and emotionally (and perhaps spiritually, for at least some people), in that the elderly are often like children when it comes to their needs. Which doesn't mean that they no longer need or deserve the dignity of adulthood (they very much do), but as far as their social and emotional needs, as they are facing death on the horizon, their needs go back to the basics: affection, validation and general caring (when all of the superficial rat race distractions of modern industrialized life are falling away).
Most of them have stories that they very much need to tell someone, which requires someone actually caring enough to ask and listen. Some of these stories are hilarious, as well, and some of them are rather emotionally deep, and some of them are "little things" stories that hold greater significance. And, sometimes the stories are angry or bitter, but you could wind up being the only person in their 60/70/80/90+ years of life who ever lets them know that it was okay for them to feel angry and that what they went through was definitely hurtful. Sometimes some pretty intense emotional processing happens at the end of one's life (I have seen it more than a few times), and all it took was for someone to really listen and genuinely care and think about what was being said, and then respond with healthy compassion.
If you can offer that to someone who is elderly and alone, then you can offer them the most meaningful thing that a human can at that stage of their life. Of course, though, again all of the practical help is very helpful, haha. It's just that deep down most of them are happier that you are there, than they are about the chores around the house getting done, if you feel my drift.
