Think of an English sentence like "It hurts when I walk too fast." Does "it" in this case mean:

_ My foot
_ My ankle
_ My knee
_ My hip
_ My lower back
_ My head
_ Possibly several or all of the above
_ None of the above; the pain is mostly in my left testicle but I'm too modest to say "testicle" in mixed company

In fact, "it" does not necessarily have any definite noun referent, and one could substitute "I feel pain when..." for "It hurts when..."

Similarly, in было солнечно, there's no implied noun like день or погода. "It" is just... "it."