Cannot make a static reference to the non-static field solved

Java Eclipse static non-static reference

I have member variables like this:

public class Solver {
  private List<Board> solutionBoards = new ArrayList<>();
  private boolean solved;

later I have codes like this:

public boolean isSolvable(){                          
      return solved;
  }
public int moves(){                                 
  int moves;  
  if(isSolvable()) {
      moves =  solutionBoards.size() - 1;
  }
  else {
    moves = -1;
  }
  return moves;
}

Eclispse says:

Cannot make a static reference to the non-static field solved
Cannot make a static reference to the non-static field solutionBoards

It offers me quick fix available:
Change 'solved' to 'static';
Change 'solutionBoards' to 'static'.

But why?

actually, I have codes like this:

  private static class SearchNode{
      private int moves;
      private Board board;
      private SearchNode prevNode;
      private SearchNode(Board board, int moves,  SearchNode prevNode){
        this.board = board;
        this.moves = moves;
        this.prevNode = prevNode;
      }
      public int getMoves() {
          return moves;
      }
      public int getPriority(){
          return board.manhattan()+ moves;
      }
      public Board getBoard(){
          return board;
      }
      public SearchNode getPreviousNode(){
          return prevNode;
      }

Finally, I saw 'static'!
I guess SearchNode class has been somehow used by those two methods below, so that's where the 'static' issue comes. I deleted the static here and there's no error anymore. I haven't really thoroughly understand the static thing yet.