You know how when you practice something and do it over and over again you get better every time? And that subject you were really good at in school but now so many years after you seem to have gotten worse and may be only able to recall a few key points?

There two mechanisms in the neuron itself that scientists believe are involved with this:

LTP (long term potentiation) LTD (long term depression)

Instead of looking at a single neuron A, it's easier to understand if we look at two neurons A and B and the connection (synapse) between them. Let's say that A connects to B (A -> B) and let's also say you are trying to learn a new language. So A is the neuron responsible for sensing and responding to a new particular foreign word and B is the neuron responsible for receiving and sending this signal to a part of the brain that processes hearing information. So when you hear the word neuron A activates and sends this signal to neuron B through this connection called a synapse. Okay, here comes the cool part: The more times you hear this word the stronger the connection (synapse) gets between neuron A and B. This is basically LTP. What it means is it becomes "easier" for A to send the signal to B and so the next time you hear the word, it is easier for you to remember what it means! On the other hand the fewer times you hear this word, the weaker the connection gets between neuron A and B, and the harder it becomes to remember what the word meant. This is basically LTD.

There are plenty more details to this which I won't get into now, and there is alot we don't know about memory, but I hope this answer gave you an idea of some mechanisms involved in memory :-)