How to explain "right" and "left" politics to a child, when most adult cannot agree on a meaningful definition? Well...
I would probably start by explaining how different people have different opinions, for many reasons, both right and wrong. Sometimes they don't know something, or they don't care. Sometimes they have different experiences. (Two people will try the same thing; one will succeed and one will fail. Will they agree about whether it was the right thing to do? Whether they should do it the next time?) Sometimes they have different preferences. (Is ice cream better than chocolate? Should we watch TV or go to the ZOO?) -- Use many specific examples.
Then I would add a warning that people can be pretty sensitive about their opinions, sometimes very irrational. It is OK to communicate with people, it is OK to learn and to teach, but when you see that someone is in a bad mood, their voice gets louder or they start insulting... then it is better to change the topic or leave. If it happens regularly with the same person, then it is perhaps better to not discuss some topics with that person. -- Again, some (non-political) examples of someone becoming angry at some discussion.
Now we are prepared for the very essense of the question: what is the difference between "right" and "left" politics. (Because so far, everything said was symmetric. Now it is time to deal with the assymetry.)
The "right" generally prefers traditional things. If someone wants to have a king, or says "let's do this, because this is what people did in the past, and it was good, so we should preserve the tradition", this would be usually labeled as the "right". Other typically "right" opinions: people are different, the smart people should decide, people should be responsible for their own actions.
The "left" generally prefers new things. If someone says "let's throw away the old customs and do it completely differently, because it was bad and we can do it much better", this would be usually labeled as the "left". Other typically "left" opinions: people are the same (their differences are the consequences of how other people treat them), everything should be decided together, people should help other people.
But these are just the general rules. No sane person is 100% "right" or 100% "left", because in different situations different things may be better. (Sometimes the new thing is better than the old one. Sometimes the new thing turns out bad. Sometimes people help each other and are happy together. Sometimes people abuse the helpfullness of others. Sometimes it is good to listen to everyone. Sometimes some people say stupid things and it is better to ignore them.) But many people do prefer one of these sides, and identify with it, just like when someone supports a specific football team. The problem is when someone becomes such a strong fan that they start hating the other side, which is a bad thing.
Again, it could be followed by specific examples of when some change was good or bad, when it was good to listen to everyone and when it was good to listen to the smart/informed one.
And then, perhaps, some specific political problems in your country could be touched gently. For example: "Some people don't have a job, so other people give part of their money to state, and state gives that money to the people without jobs. It was suggested that more money should be distributed this way. Some people think it will be a good thing, because the families of people without jobs will have more money, and can buy more useful things. Other people think it will be a bad thing, because some people may choose to stay at home and let others work for them, and the families of people with jobs will have less money than before. Can you guess which of these opinions is called 'right' and which is called 'left'? How would you approach this problem?" Remind the child that they don't have to choose only from the two extreme positions. Don't criticize the choice, but hint at some possible consequences, both good and bad. Also tell that it is OK if we can't completely solve this problem now, because adults have difficulties with this too. (The goal is not to solve a political problem. The goal is to explain what politics is, and what is political "right" and "left".)
Actually, I think that many adult people would need an explanation like this, too.