Calvin sees Hobbes a different way (alive), while other characters see him as something else (a stuffed animal).
— Wikipedia, 2007-03-15

In fact, there is a whole article on its own about Hobbes including a discussion of his reality, also quoting creator Bill Watterson:

When Hobbes is a stuffed toy in one panel and alive in the next, I’m juxtaposing the “grown-up” version of reality with Calvin’s version, and inviting the reader to decide which is truer.
— Bill Watterson, as cited in Wikipedia, 2007-03-15

I remember having discussed this issue with friends. Apparently, many (that is most if not all of my friends) see Hobbes as a stuffed animal. They think that Hobbes as a real tiger exists only in Calvin’s imaginations.
Whereas, I think that Hobbes is real as a tiger could be, and it is only other’s imagination where Hobbes is a stuffed animal.

Though, this is imaginary, of course.