The Packrat - genus Neotoma - is a type of rodent of western North America that is famous for hoarding food and other objects.
Similarly, when a human is referred to as "a packrat," the person is being described as someone who hoards objects, finding ever more creative ways to pack the maximum amount of possessions in the space available.
Example: "Jerry's a total packrat. He never throws his old junk away. His house is so packed full of old things, you can barely walk in it! He needs to throw that junk out!"
Well, as a famous proverb says, one man's trash is another man's treasure. A packrat wants to keep objects around because they could be useful in the future; thus, they are held for their potential value, not their value at the present. To someone else, these objects are junk; to the packrat, they are much more valuable. Only time can tell us if the packrat is correct in his assessments, or is simply overzealous and obsessive beyond the point of reason.