I heard the Sun is expanding with the time, will it ever explode, if not how big could it get?
It is true that the Sun is very slowly expanding and getting brighter right now. The reason for this is that as it is burning hydrogen to helium in the core the amount of hydrogen there gradually decreases. In order to keep the energy generation rate the same, the temperature and density in the core must rise. This has the effect that the energy can flow to the surface a little faster and it puffs up the outer layers (as well slightly brightening the Sun).
When the Sun runs out of hydrogen in its core completely (which won't be for another 5 billion years or so) nuclear reactions will stop there, but they will continue in a shell around the core. The core will contract (since it is not generating energy) and as it contracts it will heat up. Eventually it will get hot enough to start burning helium into carbon (a different nuclear reaction). While the core is contracting the hydrogen burning around it heats will heat up the outer layers which will expand, and while they do that they will cool. The Sun will then become what is called a Red Giant and its radius will be large enough to envelop the Earth!
Eventually the Sun will also run out of helium in its core. When this happens the core will contract again, but it will never be able to get hot enough to start burning any other elements into anything else. There will still be nuclear reactions of helium and hydrogen in shells around the core though, and these will continue to heat up the outer layers and cause them to move outwards. The core will eventually turn into what we call a white dwarf star, which is an extremely small (roughly Earth sized) dense star. A white dwarf does not generate energy so it will just slowly cool as it shines. The outer layers of the Sun will turn into what we call a "planetary nebula" (although it has nothing to do with planets) and gradually drift out into the interstellar medium. Planetary nebulae are some of the most beautiful objects you can see in the night sky. Shown below is the ring nebula, for some more pictures look here.
So the Sun will never explode (even though more massive stars can and do). The difference is that the Sun isn't massive enough to ignite anything past helium in its core. More massive stars continue nuclear burning until they start making iron. This creates an unstable core which will then explode in a supernova explosion.
Last updated Feb. 10th 2016