Visual tracking
The ability to follow an object with your eyes is an important skill, and you'll see this in action when they are older and they watch a ball as it is thrown to them so that they can catch it, and follow text with their eyes as they read.
For now, your baby's greater control of their eyes and head means they can watch a moving object and turn their head so that they can continue to watch it as it moves past them. Your baby is likely to be able to track an object more smoothly now and also be able to keep watching an object that is moving a little faster.[1]
Preferences and attention
Up to this point, your baby will have been most interested in looking at faces, but as they develop they will begin to show an interest in different toys and objects.
Researchers have explored if babies visual track an item for longer if they are more interested in it, and studies do suggest that babies might prefer certain visual stimuli and track these for longer. This indicates that babies begin to gain control of their attention and will choose what to look at and follow with their eyes.
Distance and decisions
Your baby’s vision will continue to develop and they will be able to watch things that are further away. They will be able to look at objects to learn about their features and will begin to recognise objects represented in pictures. Your baby will develop their ability to pay attention to a particular visual stimulus and to choose when to stop looking at something.
References:
[1] Game, F. Carchon, I. Vital-Durand, F. (2003) ‘The effect of stimulus attractiveness on visual tracking in 2-6 month-old infants.’ Infant behavior & Development. 26 (2003) pp135-150.