Arcturus is an example of a red giant star. To understand giant stars, we need to know a little bit about stellar evolution. Stars spend the majority of their lives fusing hydrogen into helium, and it is these nuclear reactions that cause stars to shine so brightly. Our Sun has spent about 4.5 billion years fusing hydrogen in its core and will spend roughly another 4.5 to 5 billion years doing so until its supply of core hydrogen begins to run out. (Yes, our Sun is middle-aged.)
As hydrogen fuses in the star's core, it is transformed into helium. Eventually (as in billions-of-years-eventually) the star will have a mostly helium core surrounded by a shell of not-yet-fused hydrogen. At this point the hydrogen supply in the core is getting low, so the nuclear reactions slow down and the core shrinks. As the core shrinks, it gets really hot- hot enough for the not-yet-fused hydrogen in the shell surrounding the helium core to, well, fuse. At this point we have a star with an inert helium core (helium that isn't fusing into anything), and a hydrogen shell that is fusing surrounding the helium core.
The intense heat from the hydrogen fusing shell pushes the star's atmosphere out to an enormous size, causing the outer atmosphere to cool. Because the star is bigger, it becomes more luminous, and because its cooler, it appears red, or, like Arcturus, a lovely shade of stellar orange.
Arcturus will keep up the red giant situation for roughly a billion years. The giant name is apt. Arcturus currently has a diameter just over 25 times that of the Sun. This is enormous, but there are stars that can become even larger. The larger giants are called, not surprisingly, supergiants. A star has to start out with more mass than than the Sun (or Arcturus) to become a supergiant star. Betelgeuse in the constellation Orion, for example, is a supergiant. It has a radius 950 times that of the Sun and would engulf Mars if it was put in the place of the Sun.
And speaking of the Sun, our parent star will eventually become a red giant like Arcturus in about 5 billion years. It's outer atmosphere will cool making it appear reddish, and its larger size will give it a luminosity 1000 times what it is today and Earth will be cooked, literally.
Really, though, things will get bad for Earth before the red giant phase. The Sun is getting gradually hotter, and in about 3 to 4 billion years the Earth's oceans will boil away. Hopefully we'll be able to find another place to live. Saturn's moon Titan is looking awfully good right now.