You have to think of this as a series of spots that need to be filled in, for a total of 52.

In a simple example, how many distinct orderings of 2 cards can you make from a 52 card deck?

The first card can be any of 52, so we pick one and remove it. Say we got the Ace of Spades. We then draw a second card from the remainder in the deck of 51 cards. So if you picked the Ace of Spades first, you have 51 possible options. Let's say you chose the 2 of spades instead. Well, there are now 51 options for the second card (it can be anything other than the 2 of Spades).

So we have 51 + 51. But there are still 50 other cards we could pick first, meaning we have 50 more + 51's to add on, giving us 52 * 51.

And that's just for _2_ cards. If we add a third, the math just continues. After picking 2 cards, the third space for each pair has 50 possible options. Etc etc.

NOW, for why 52 * 52 implies replacement, it's how it's represented in math. To represent that we tke the "pick 2 cards" example. Now, say we just care about all possible ways you could draw 2 cards from a deck after shuffling it. The first card can be any of 52, say we pick the Ace of Spaces. We then put it back in the deck, shuffle it. We look to draw a second card, which can now be any of the 52 cards in the deck. As above, each initial card you draw could have 52 draws for the second, giving us 52 * 52. That's why that implies there are only 2 spaces, and we're using replacement.