The Time Machine has two main threads. The first is the adventure tale of the Eloi and Morlocks in the year 802,701 AD. The second is the science fiction of the time machine.
The adventure story includes many archetypal elements. The Time Traveller's journey to the underworld, his fear of the great forest, and his relationship to Weena, mirror imagery prevalent in earlier literature, imagery strongly associated with the inner workings of the human psyche.
The tale of 802,701 is political commentary of late Victorian England. It is a dystopia, a vision of a troubled future. It recommends that current society change its ways lest it end up like the Eloi, terrified of an underground race of Morlocks. In the Eloi, Wells satirizes Victorian decadence. In the Morlocks, Wells provides a potentially Marxist critique of capitalism.
The rest of the novella deals with the science fiction of time travel. Before Wells, other people had written fantasies of time travel, but Wells was the first to bring a strong dose of scientific speculation to the genre. Wells has his Time Traveller speak at length on the fourth dimension and on the strange astronomy and evolutionary trends he observes as he travels through time. Much of this was inspired by ideas of entropy and decay promulgated by Wells's teacher, Thomas Henry Huxley.
I think it's important to realize that when the time traveller leaves in the end, he has with him a bag and a camera, so the reader can infer that he will return with proof.