In CSS, `height` and `width` are properties used to define the dimensions of an element. `height` sets the vertical size, while `width` sets the horizontal size of the element. You can use various units like pixels, percentages, ems, rems, and more to specify these values.
For example:
```css
.element {
height: 200px;
width: 300px;
}
```
`max-width` is another CSS property that limits the maximum width an element can have. It prevents an element from exceeding the specified width even if its content would normally cause it to expand further.
For example:
```css
.element {
max-width: 500px;
}
```
Using `max-width` is helpful for making sure your layout remains responsive and prevents elements from overflowing their containers on smaller screens or when the content is too large.