The Time Traveller (the main character) has built a machine capable of transporting humans through time. At first, he only goes forward by a couple of hours. Nothing great.
Then, as reason would have it, he decides to jump forward a little bit. By a little bit, I mean More than 800,000 years into the future. In the year 802,701, the world has changed significantly. The Traveller comes across the Eloi and the Morlocks, two post-human races that are at odds with each other. The Eloi live above ground, while the Morlocks live underground (much like Wells did for a significant part of his life; he and his family would often spend time underground in his formative years). As luck would have it, the Traveller has to go on a bit of adventure when the machine is taken by the Morlocks. When he gets it back, he explores another time: 30 million years into the future. Startled by what he has seen, he returns to his own time.
Towards the end, the Traveller goes on another trip, promising to return shortly.
You can purchase a hard copy of the book here. A sequel to the book, The Time Ships, can be bought here. Back to the Future is probably the most famous film influenced by The Time Machine, but anything that includes time travel can said to have been influenced by it in some way, shape, or form.