Good atari - bad atari
In this diagram, Black is trying to establish something in White's sphere of influence.
is a bad atari, because it will end up captured and serve little purpose. White can now severely attack (a) and though will provide some aji while running, Black could have used this move better.
This sequence is not as catastrophic, but White's outer strength combines well with the rest of his sphere of influence. This atari is tactically OK, but strategically maybe not as interesting (we should see the whole board to judge that).
kokiri's idle thought - In this diagram Black will potentially have the option later in the game of playing an atari at a instead of the previous one at b. As a is less deeply inside whites area, it will thus have more aji.
 White has to reinforce eventually at , which results in better shape for black, than if White had skipped and extended directly with . is not an atari, but gives the same impression.
It could be called bad pre-atari.
looks to the point e.
 continuating from above problem diagram ,
White would use the chance to get influence. IMO the aji of Black a can be coped with Wd.
Of course, Black could think of making sabaki with e-f actions. The point here is not to discuss these later options, rather to show White's influence --.
After Wg & h one starts discussing killing black.
Could purists argue that also is a bad atari and aji-keshi? I think not, the advantages are too much.
Tderz: Wa-Bb and Wc-Bd are miai pairs
and sacrifice the marked stone with the highest possible gain, then White ties it together with . The order of play matters here:
This order of and leaves Black the option to take the outside with . As Black has the choice, it will generally favour him when he does take this option. To complete the argument ...
Black has options here too, but this one is dangerous and not preferable. White's stone will provide bad aji for Black all over the place.
See Atari atari.