iVenky, to gain some knowledge of such basic things as offset and drift, it's best if you first do your own reading from books and websites rather than ask about everything in forums. One reason is that you will often gain a better understanding if you do your own reading instead of being spoonfed the answers. Another reason is that, frankly speaking, having to explain such basic matters over and over again is a big burden on more experienced people.
There must be plenty of articles, online and in books, about offset and drift. If, after making some effort, there are still some points you don't understand, then ask in a forum and people who know will be glad to help. Having said that, here's a brief explanation of offset and drift:
In an ideal opamp, when the inverting and non-inverting inputs are at the same potential, the output should be exactly half-way between the positive and negative supplies. If the opamp has a balanced +/- power supply, the opamp output should be at zero volt. If it has a single-ended supply, that is, + and ground, then the output should be at exactly half of the supply voltage. In the ideal opamp, the output should be off the half-way point only if there's a voltage difference between the two inputs.
However, a practical opamp behaves differently. To have the output mid-way between the + and - power supply, it always needs a small voltage difference between the inverting and non-inverting inputs. This small voltage difference which is needed to balance the output is called the input offset voltage. The offset voltage of many general-purpose opamps are of the order of 1-5mV whereas precision instrumentation opamps may have an offset of much less than 100uV.
There's also input offset current. The meaning is the same except that it's about the input bias current rather than voltage.
The term "drift" can be applied broadly to many things. In general, it means a state or property that changes by itself with time without user control. It is most often caused by a change in temperature but may also be caused by material aging. When applied to opamp offset voltage, drift is the gradual change in offset voltage without any external input.