Translation:The Russian man hurries to the cold water and jumps into the water.
Just "siet" lacks that sense of completeness that the man actually arrives at the water. "Odasiet" gives us that satisfaction. The man hurries and ends up being at the water. So now he can jump in. Many of these preverbs serve the purpose of giving the verb a sense of completeness. Of making it a completed action.
Well, partly, because many of the preverbs also indicate direction. For example:
"felmászik a fára" - climbs up onto the tree
The preverb "fel" is "up", and the suffix "-ra" is "onto".
How about we say the preverb indicates the direction and completeness, and the suffix indicates the destination? That is also not perfect, but maybe close to the truth.
These are directional preverbs: le-, be-, ki-, fel-, el-, át-, rá-, ide-, oda-.
But some of these can also be absolutely non-directional.
And there are ones that have nothing to do with direction, their main purpose is to show completeness. The best example is "meg-". It has no actual meaning that I can think of. Yet it is a very common preverb.
Yes, language can state the obvious sometimes. You can also say "I go into the house and look out the window" when it is obvious that you can't look out the window from outside the house.
But "siet a vízhez" gives the sense of "is hurrying to the water", ie. that it is in progress. So, how can he jump into the water when he is still on his way to the water?
But you can say "a vízhez siet" and you will be fine.
See, this "perfective aspect" is not about things that already happened. No. It is simply looking at the whole, complete, action, whether in the past, present or future. The sentence above describes twoof these complete actions: the man walking over to the water and the man jumping into the water. That is all. And the means of achieving this is using a preverb, usually. The "arrival" is coded in the perfective aspect of "odasiet".
You have to give your mind some time to wrap itself around this phenomenon. English does not really have this (or only to a lesser degree), so it can surely be totally weird and seemingly pointless. And it may continue to feel weird long after you accept and understand it. But then, one day, it will totally make sense.