When I use my web browser, I am usually doing a search. I am rarely typing a URL from memory. Also, I try doing everything through my keyboard. Using my mouse means thousands of back-and-forths with my right hand every day, which cost me time and energy. And sometimes I have to look at the mouse to grab it, which makes me lose my focus on the things I was doing on the screen. For what I do, all-keyboard is better.
Up to Firefox 33, my typical web-search steps were: 1) alt-tab to web browser, 2) ctrl-K to focus on the search bar, 3) ctrl-down to select the appropriate search engine, 4) type query and enter. Step 3) is a power user step. Its goal is to save time by not using the mouse and skipping a web page load. For example, I want to know who Seth Green is. I could run the search through Google or DuckDuckGo, and then click the Wikipedia link (usually in the top 3 results). But if I select Wikipedia as my search engine, I directly land on the page for Seth Green. So ctrl-down saves me a page load and a mouse click. Some users even have more than 30 engines!
In their new search interface, called Find it Faster, FF34 basically replaced ctrl-down by a mouse click on tiny buttons. FiF saves me a page load, but it's at the cost of a mouse click. Below is a GIF demonstrating the new search feature.
Average users do not switch search engines - they always use the default one. So FiF is a feature targeted to power users, and yet it apparently forces them to use their mouse. Obviously, the feature has annoyed many users, including me.
There are two solutions. A first solution is rejecting the change: go to about:config, and switch browser.search.showOneOffButtons to false. Another solution is learning the change: the search steps used to be 3) ctrl-down, then 4) type query and enter. Now the steps are 3) type query, then 4) press tab to switch search engines, and enter. This new process is not as good as the old one: switching search engine after having typed, rather than before, loses the benefit from autocomplete/search suggestions anymore. Anyway, Mozilla should emphasize on their FiF release page that tab replaces ctrl-down.
Edit 3/17/2015: to disable it, go to about:config, and turn