The notation is a little unusual, but not radically so. It could have said simple to hold the G, and in the other measure the C, but the way it is said is a little more specific. Whichever, it is important to indicate which note in the figure is to be held.
And why a hold instead of adding a note? Because the hold is not intended to be specific, but is intended to be a slight stretch in the pulse of the music at that point, with that specific note being the note involved in the stretch. Note that all the other notes which are sounding at the same time are also held at that point! If one were to add a note to the G (or C) one would have to add the same time to all the other notes -- which would mean, from the writing it down standpoint, that one would also have to change the time marking for that measure, and that measure only, to accommodate the extra note. Which would be a mess.
The length of the hold is an artistic decision. The idea is to give a slight emphasis to that note (without making it louder) or a slight pause in the pulse of the music at that point -- and how much to do that is entirely up to the artistic decision of the performer. Sometimes a hold is only a barely imperceptible stretch in time. Sometimes it can go on for quite some time, relatively speaking. It can even be influenced by the instrument one is playing, as well as one's artistic judgement -- for example, there is a hold on a chord in one Nocturne which I play which I hold as the tone dies away, until the volume of sound remaining matches the volume of the next note I am going to play; this time differs on various instruments.