In this example all the eighth notes are played off the beat. Playing off the beat creates an effect known as syncopation, which means displacing the normal flow of accents (usually from on the beat to off the beat). Syncopated rhythms can be difficult at first but are very common in keyboard playing, so stick with it. Count and tap your foot to keep time as you play.
Here are some more examples of parts created by the use of eighth rhythms starting off the beat.
Once you are comfortable playing chords in eighth note patterns, try playing them as broken chords with the right hand while playing alternating bass notes with the left hand as shown in the following examples. This is probably the most common accompaniment style in Country music.
This one is a common ^ time variation.