Wikipedia
In American football, a checkdown pass is when the quarterback attempts to complete a short, accurate pass to a running back or tight end as a last option when the wide receivers are covered. The term means that the quarterback has "checked down" his list of receivers. Because the quarterback does not look for the checkdown pass until after he has scanned for open wide receivers down the field for about 3–4 seconds, the defensive line has had time to enter the backfield and so a checkdown pass is often thrown in the face of pressure from the defensive line. Alternatively, if the quarterback is inexperienced or the defensive team has sent a blitz, with linebackers and/or defensive backs also looking to sack the quarterback, the checkdown may also turn out to be the quarterback's second or even first look. These plays often result in significant yardage gain, because most of the defensive players are either in the backfield in pursuit of the quarterback, or deeper in the secondary covering receivers.
A screen pass and a checkdown are different.