What is this brown liquid that I got when I boiled glycerol and water solution?
If your mixture reached 160 degrees C then you must have boiled off all the water. If there was some water left, it would stay at around 100 degrees C and all (most of) the heat would be used to evaporate water.

The boiling point of glycerol is about 290 degrees C and so you didn't boil that off. I disagree with @Skeptical Chymist about you making the caramel (for the sake of god, don't eat it to test it out). Not all that gets brown is caramel and there were no sugars there I presume. If i had to guess I'd say that at 160 C you've managed to completely obliterate any complicated organic structures and what's left is glycerol, charcoaled bits of any organic impurities that you happened to have in the starting material and possibly some acrolein which is a common product of dehydration of glycerol (you can recognize it by it's smell).

Overall; it's hard to tell what one gets, when they heat the hell out of something.