I have Trek 1.1 with currently 700*23C tyres.
I need to replace them but the one available in market are 700*28
Can I use this size as replacement?
If yes, what'll be advantage and disadvantages?
Your rims can almost certainly take the extra width. The real question is can your frame, forks, and brakes? Only you can measure that.
Based on nominal dimensions (and some approximations) you would need an extra:
5mm above (to clear the brakes) and in front of the back tyre.
A few bikes even have the front wheel very close to the downtube. This assumes a very similar tyre to the one you have, just a bit bigger. You need to add a bit for safety margin, plus you need some clear air between the new tyre and the frame. So do you have enough clearance around the tyre?
The 28 should give a slightly more comfortable ride, and may even be more efficient. You'll need a slightly lower pressure.