What does `&#my-id` mean in CSS or SASS?

It refers to the parent selector.

Input:

.parent {
    &.child {
        color: red;
    }
}

Output:

.parent.child { color: red }

It's really helpful if you're writing CSS in BEM format, something like:

.block {
    &__element {
        width: 100px;
        height: 100px;
        &--modifier {
             width: 200px;
        }
    }
}
.block__element { width: 100px; height: 100px;}
.block__element--modifier { width: 200px;}
<div class="block__element"></div>
<div class="block__element block__element--modifier"></div>

And finally, all examples I've shared have been concatenating the class names, but you can also use it as a reference, like:

.parent {
    & .child {
         color: red;
    }
}
.parent {
    .child & {
         color: blue;
    }
}

.parent .child { color: red }
.child .parent { color: blue }

Additional references:

http://lesscss.org/features/#parent-selectors-feature

https://blog.slaks.net/2013-09-29/less-css-secrets-of-the-ampersand/

Using the ampersand (SASS parent selector) inside nested selectors

It's a built-in feature of Sass: https://css-tricks.com/the-sass-ampersand/

You can use it when you're nesting selectors and you need a more specific selector, like an element that has both of two classes:

If your CSS looks like this:

.some-class.another-class { }

And you wanted to nest, the Sass equivalent is:

.some-class {
     &.another-class {}
}