Delay is an effect inside of Atom that repeats your sound over time. The section is found on the FX section of ATOM:

To turn the Delay section on either click the grey power icon on the top right of the Delay module, or click the light to the left of the Delay rack of the FX module section:

When the light is blue it means the Decay section is turned on.

"Time L," and "Time R," determine at what interval the delays occur. The chosen delay interval is shown below each knob, and higher values mean the delay will occur more frequently. 

The Delay times of the L and R signals can be linked together with the Link button, which will make both the same interval whenever one is changed:

"Decay," controls how long the delays continue. Turning this knob to the right will cause the delay to repeat more often, making the delayed sound take longer to disappear.  

The "Mix," control acts like a dry/wet function, meaning the higher the amount the more of the Decay effect will be applied to your sound. An Amount of 0 essentially means the delay is inactive, but turning the Mix knob to the right will make the delay effect louder and more noticeable.  

The "Sync," button syncs the delay's Rate to the BPM of your song. For example, if the Sync is engaged (turned to the right) your Time L and Time R options will be displayed as divisions of the beat (1/4, 1/2, 1/8, and so on). With Sync disengaged the Time L and Time R options will be shown in milliseconds.
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"Ping-Pong," alters the delay type to be a ping pong delay, which has a different sonic characteristic to the normal delay. It uses stereo tricks to make the delay seemingly bounce from left to right and vice versa, which can be a great effect.