Chemistry - Why do cotton clothes take a longer time to dry as compared to synthetic clothes?

Cotton fiber is primarily cellulose:

The red atoms are oxygen, and the white atoms are hydrogen. Whenever you have hydrogen attached to something extremely electronegative (such as oxygen), there is a potential for hydrogen bonding to occur:

As you can see, the electronegative oxygen atom draws electron density away from the more electropositive hydrogen atom, which results in a very polar bond. The positive charge on one molecule attracts the negative charge on another, and a very strong physical bond forms.

Now compare cellulose with something like nylon:

Since water can hydrogen bond to cellulose, it "sticks" much better - we say that it is hydrophilic. Since it can't form hydrogen bonds to nylon, we say nylon is more hydrophobic.

The same is true for most synthetic polymer fibers, and as a result, cotton absorbs water much more readily than other fibers, and tends to "hang on" to the molecules for longer - which means cotton fibers take longer to dry.