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Here was my explanation for why I'm interested in Subfactors, which has a different flavor than the my other answer abovefor why "people" are interested in them:

Subfactor planar algebras are just unitary versions of something very natural. For example, they're unitary versions of 2-categories with 2 objects (tensor categories are 2-categories with 1 object, so this is a natural next step). Also they're just the unitary versions of a simple algebra object in a tensor category, so if you like simple algebras (and who doesn't really) then you'd like subfactors. The unitarity assumption is convenient for computations and thus is convenient to assume when you're trying to find new examples. Also the subfactor literature has lots of results which have applications to tensor categories, but written in a totally different language, so it's worth learning what subfactor people are talking about.
show/hide this revision's text 1

Here was my explanation for why I'm interested in Subfactors, which has a different flavor than the answer above:

Subfactor planar algebras are just unitary versions of something very natural. For example, they're unitary versions of 2-categories with 2 objects (tensor categories are 2-categories with 1 object, so this is a natural next step). Also they're just the unitary versions of a simple algebra object in a tensor category, so if you like simple algebras (and who doesn't really) then you'd like subfactors. The unitarity assumption is convenient for computations and thus is convenient to assume when you're trying to find new examples. Also the subfactor literature has lots of results which have applications to tensor categories, but written in a totally different language, so it's worth learning what subfactor people are talking about.