What causes electrical outlets (receptacles) to stop working - there are many reasons why something like this can happen so the first thing we have to do is process of elimination so we can narrow down the causes.
Since you are very limited in residential electrical experience we can only offer just so many suggestions before you have to say "this is beyond my ability". It is ok to admit this when the time comes. It could be something very simple or it could be something complex.
Just like when you go to the doctor you can't just say you don't feel well and you expect the doctor to know what is wrong with you. You have to give as many symptoms as possible to narrow down the possible cause.
It doesn't have a reset button either.
There does not have to be a reset button on the receptacle itself. If this receptacle and light is on a circuit which is protected by a GFCI upstream this could cause the circuit after the GFCI receptacle not to work if the GFCI receptacle tripped (the GFCI receptacle if this is the problem does not even have to be in the same room).
Narrow down the possible cause:
#1 - Besides this light fixture and this receptacle you show in the pictures is there anything else so far that is not functioning?
#2 - Have you checked to see if a breaker tripped in the breaker panel? Do you know how to test/see if a breaker has tripped?
#3 - I would go to each GFCI receptacle in the entire house and press the "Test" button and then the "Reset" button on every one of them. Use the very tip of your finger to press firmly inward on these buttons. Yes, every one; does not matter it's location in the home compared to where this problem is located. This is what an electrician would do to start with along with making sure no breakers tripped in the panel.
Once you check these 3 things get back to us and let us know your findings. If you find any GFCIs that you can not reset make note of where they are located.