karma- essentially every action has an equal reaction. there are different ways to interpret this. the buddha taught about karma in this life. this kind of karma is a factual thing that cannot be denied. i'll give a hypothetical example to explain: if a person steals something they will worry they will be caught. this worry is a negative feeling and could be called negative karma. doing bad things like this create people that do not like this person and even if they don't know who the person is it has created negative feelings in them which will effect the world through their actions. the more negative actions someone does the more worry and guilt they accrue. they also build up more and more people that don't like them and may cause them problems. this is concrete. doing many bad things affects a person negatively emotionally and usually affects the physical world in ways that are problematic for them as well. the next i will say is plausible, but it's a theory more than anything: a thief may forget their crimes but later in life they may worry again when reminded of what they stole or subconsciously set themselves up to be stolen from out of repressed guilt by leaving their wallet on a car seat with the doors unlocked or something similar. the buddha described us as containing a storehouse of past karmas. this could be likened to the subconscious mind. we create consequences and results for ourselves based on our actions. karma is described as an ever changing thing that builds on itself. this kind of thought can be applied to any action we take.
good karma is obvious, an example: help your neighbor rake his/her leaves and they will be likely to help you in the future. do good things and people will like you more and you won't worry as much. etc.
now there is also karma that is more mystical in explanation. the idea that we cycle through different realms of existence and have been doing so for an unknowable, seemingly infinite amount of time is tied to this kind of karma. our actions from past lives affect our current lives. when bad things happen to good people it is because they are reaping what they have sown in previous life times. let's say there is a nice man who is a manager at a restaurant. he is kind to the employees beneath him and always has been. but the manager above him is very mean to him, the likely explanation is that probably he was a mean manager in a past life.
now karma keeps going and we keep making more. karma is also what keeps us here in the six realms. the eightfold path is the key to creating no new karma. following it creates only good and neutral karma. thus if a person dies before reaching enlightenment they are likely to be reborn in circumstances that are positive and conducive to practicing buddhism and achieving it's goals. after a person has achieved enlightenment using this path they create no new karma whatsoever and are therefore free from the cycle.
the explanations of rebirth are pretty predictable. for example when asked how to be reborn and meet and marry the same person again the buddha simply explained that a couple should be very good to each other in this life and this love and devotion would make them meet again in the next. i will write a post specifically to explain rebirth soon.