Potentially silly question about the way game review explains missed checkmate

I'm pretty terrible at chess, I started learning last night through the lessons on here. I can win against Martin, but it takes me FOREVER because I just barely understand checkmate. I've been using the game review feature to see how I can checkmate faster because it honestly takes me like 30 turns even when the opponent only has a king (don't laugh it's been one day!). What I'm wondering is, based on the game review, I should be able to checkmate MUCH sooner, but when I try to do this myself, I always end up in a stalemate because the king wasn't in check. But the game review always prompts me to enter into checkmate even when the king isn't in check. I don't understand at all. Is there some way to skip checking the opponents king? 

I would attach an image of the game review's suggestion but the forum isn't letting me!! Maybe because my account is new?

Please answer in simple terms, like you would for a kid or something. I'm 19 but in the chess world I think I'm about an infant. 

Maybe this will work. Game review suggests that I move my rook from b8 to a8 for checkmate but the white king isn't in check? Won't this make a stalemate?

Nevermind the board won't upload. Ignore this comment

In end games where you are outright winning, don't worry about the fastest possible checkmate. Just ensure you have an unstoppable plan. Mostly by trapping the king with a rook or queen.

For instance here, this isn't the quickest way to checkmate but you can see the idea. The king can never walk past the rook, so you slowly but methodically push the king into a corner. Once they are on the edge, you just look to check them with your rook while your king takes over the job over keeping them on the edge to create a checkmate. The above is a really common end game idea, as you either have a rook or queen and can use this, or you don't in which case you probably want/need to promote a pawn into a queen to win (if you have no rooks, queens, or pawns you are going to have a very hard time checkmating) so learn and practice this pattern until you feel confident in it.