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H2O and H2S are both bent molecules and are therefore polar. And while H2S molecules are attracted by dipole-dipole interactions, water molecules are attracted by hydrogen bonds which in this case are much stronger. 

Hydrogen bonding only occurs when hydrogen is covalently bonded to a small, highly electronegative element. These are N, O and F. The N, O, or F distort the bond to hydrogen sufficiently so that H can form a weakly covalent bond with another N, O or F atom in an adjacent molecule. This is the hydrogen bond, the attraction between molecules. 

Since the attraction between molecules is stronger in water than in H2S, water will have higher melting and boiling points. 
Whether a compound will be a solid, liquid or gas at a given temperature can be explained by the attractive forces between its molecules. 

H2S (hydrogen sulfide) is a gas because at room temperature the forces and interactions between the molecules of hydrogen sulfide are very weak. 

The water molecule has a stronger dipole (a negatively and positively charged end to the individual molecule) so these negative and positive ends continually attract each other like magnets of opposite poles, creating more cohesion between the molecules of water