It means that every state will be entitled to have its two senators vote to block or uphold a Constitutional amendment. There was a great deal of concern in 1787 that in a popularly-elected government large states ( like Virginia) would be able to dominate the smaller ones, that a majority could tyrannize a minority. The equal representation in the Senate was designed to keep that from happening, and here it is spelled out very clearly that this equal representation can't be taken away- that, say, an amendment can't be passed over the objections of smaller states by taking away their senate votes.

Senators would be appointed by state legislatures until 1913. The framers wanted to have the Senate formed from representatives chosen by the governments of the states, not by people directly elected by their citizens. So, in answer to your question, the framers were thinking of Senators as representing more of the will of the state governments, here, than their citizens.