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There are certain things that only work in maths mode. If your document is not in maths mode and you have an _ or a ^ character, TeX (and by inheritance, LaTeX too) will say

! Missing $ inserted

as if you couldn’t possibly have misunderstood the import of what you were typing, and the only possible interpretation is that you had committed a typo in failing to enter maths mode. TeX, therefore, tries to patch things up by inserting the $ you ‘forgot’, so that the maths-only object will work; as often as not this will land you in further confusion.

It’s not just the single-character maths sub- and superscript operators: anything that’s built in or declared as a maths operation, from the simplest lower-case \alpha through the inscrutable \mathchoice primitive, and beyond, will provoke the error if misused in text mode.

LaTeX offers a command \ensuremath, which will put you in maths mode for the execution of its argument, if necessary: so if you want an \alpha in your running text, say \ensuremath{\alpha}; if the bit of running text somehow transmutes into a bit of mathematics, the \ensuremath will become a no-op, so it’s pretty much always safe.