SpaceX is an American commercial space company that has contracts with NASA to produce rockets capable of delivering payloads to space. Among those, are spacecraft that take astronauts to and from the International Space Station, as well as supplies for those who are already there.
In the future however, SpaceX hopes to use their talent as rocket scientists to someday put mankind on the red planet: Mars. This is a goal that is shared by NASA, and is hoped to be achieved within a couple of decades.
Elon Musk, the man behind SpaceX, has said he believes we can put people on Mars as soon as 2025, but more realistic estimates from NASA say this would happen closer to 2030 or 2040. There is just a lot of technology that needs to be developed to ensure that astronauts can survive for long periods of time in a hostile environment like that on Mars.
Getting us there is another thing entirely. Current rockets are not capable of taking mankind to Mars with the supplies they'll need, mostly because of the weight/fuel ratio. Future rockets will be far more powerful and provide the additional thrust necessary with a not-so harsh economic backlash in the cost of fuel.