I think I could give some intuitive look on SR. It is not very hard to understand the basic overview of SR. There are only two postulates and not more that that..! But, there are many sites which provide a bit wrong infos. And, Whooo - found it... Your question is just a duplicate.
First postulate: "The laws of physics hold good (are the same) in all inertial frames of reference".
First of all, SR declares that all motions are relative. Mass, length, space & time, etc. are not independent but they are all inter-dependent according to Einstein's view which discarded absolute space and for now, it is treated obsolete.
Say for example (the most basic one) - You and your friend are traveling in parallel but exactly the opposite direction at speeds $v_1$ and $v_2$. Relative to you (you are a rest frame now), your friend would be past you at $v_1+v_2$. Both of you would experience some effects (mentioned below) and would also measure different distances, time, etc. The physical laws would be the same because you guys are in an uniform motion. If both were racing each other, one would measure the other's velocity as $v_1$ ~ $v_2$. And, another thing I'd like to note - If both travel near $c$, you'd have to take Lorentz factor $\gamma$ into account. So, you'd have $\Delta l,\Delta t, \Delta m$ and even relativistic acceleration. But, these are noticeable only to the worst cases (like above $0.5 c$).
Second postulate: "The speed of light ($c$) is the same in all inertial frames of reference".
Wherever you both go, you guys will measure the speed of light to be the same value $c$ because you guys are still in inertial frame. This postulate is perhaps given a greater priority because it specifically says that information could not be transferred at velocities above $c$.
Thus, SR concluded some new facts like slowing time, shorting length, apparent mass, Could Faster than light be possible?, got stuck by a twin paradox, the possibilities for faster than light, etc., etc... A great thing to note is - all these effects could be experienced by you only if you travel comparatively near $c$. Oh... And the most important ones - Mass-energy equivalence, Space-time and Lorentz transformation.
For more info, please refer the duplicate one. A best reference would be a Simulation. Once you have some basic understanding on SR, please see Real Time Relativity. It is totally amazing. Of course, I found it (some time ago) in Lubos' blog.
Note: Gravity also affects objects. Actually, the effect of gravity on objects were generalized by Einstein to expand SR to GR (took some years though)