CSS selectors ul li a {...} vs ul > li > a {...}

ul > li > a selects only the direct children. In this case only the first level <a> of the first level <li> inside the <ul> will be selected.

ul li a on the other hand will select ALL <a>-s in ALL <li>-s in the unordered list

Example of ul > li

ul > li.bg {
  background: red;
}

<ul>
  <li class="bg">affected</li>
  <li class="bg">affected</li>    
  <li>
    <ol>
      <li class="bg">NOT affected</li>
      <li class="bg">NOT affected</li>
    </ol>
  </li>
</ul>

if you'd be using ul li - ALL of the li-s would be affected

UPDATE The order of more to less efficient CSS selectors goes thus:

• ID, e.g.#header
• Class, e.g. .promo
• Type, e.g. div
• Adjacent sibling, e.g. h2 + p
• Child, e.g. li > ul
• Descendant, e.g. ul a
• Universal, i.e. *
• Attribute, e.g. [type="text"]
• Pseudo-classes/-elements, e.g. a:hover

So your better bet is to use the children selector instead of just descendant. However the difference on a regular page (without tens of thousands elements to go through) might be absolutely negligible.

ul>li selects all li that are a direct child of ul whereas ul li selects all li that are anywhere within (descending as deep as you like) a ul

For HTML:

<ul>
  <li><span><a href='#'>Something</a></span></li>
  <li><a href='#'>or Other</a></li>
</ul>

And CSS:

li a{ color: green; }
li>a{ color: red; }

The colour of Something will remain green but or Other will be red

Part 2, you should write the rule to be appropriate to the situation, I think the speed difference would be incredibly small, and probably overshadowed by the extra characters involved in writing more code, and definitely overshadowed by the time taken by the developer to think about it.

However, as a rule of thumb, the more specific you are with your rules, the faster the CSS engines can locate the DOM elements you want to apply it to, so I expect li>a is faster than li a as the DOM search can be cut short earlier. It also means that nested anchors are not styled with that rule, is that what you want? <~~ much more pertinent question.

">" is the child selector

"" is the descendant selector

The difference is that a descendant can be a child of the element, or a child of a child of the element or a child of a child of a child ad inifinitum.

A child element is simply one that is directly contained within the parent element:

<foo> <!-- parent -->
  <bar> <!-- child of foo, descendant of foo -->
    <baz> <!-- descendant of foo -->
    </baz>
  </bar>
</foo>

for this example, foo * would match <bar> and <baz>, whereas foo > * would only match <bar>.

As for your second question:

Which one is more efficient and why?

I'm not actually going to answer this question as it's completely irrelevant to development. CSS rendering engines are so fast that there is almost never* a reason to optimize CSS selectors beyond making them as short as possible.

Instead of worrying about micro-optimizations, focus on writing selectors that make sense for the case at hand. I often use > selectors when styling nested lists, because it's important to distinguish which level of the list is being styled.

_{* if it genuinely is an issue in rendering the page, you've probably got too many elements on the page, or too much CSS. Then you'll have to run some tests to see what the actual issue is.}