In Game of Thrones S08E01, Cersei was so disappointed for not getting elephants and it's being part of so many memes and joke now.

But why does elephant matter? Her competition/rivalry is with Daenerys/Starks etc. And they have dragons. So what purpose elephants can fulfill? What is the significance of this obsession?

It seems they were a kind of Easter-Egg.

In the novels, we received a long narrative about the elephants of The Golden Company, which was left out of the show.

In George R. R. Martin’s fifth GOT novel, A Dance With Dragons, we learn of The Golden Company through a rather long-winded side story that has thankfully been cut from the HBO show lest it get even more complicated. Someone in the writer’s room clearly wasn’t happy with this decision, and so decided to throw in an elephant-sized easter egg for viewers who have also read the series so far.

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_{Cersei’s need for elephants in the Game Of Thrones premiere comes directly from the books - Metro UK}

So, it seems like this is a special Easter-Egg for those who have read the series.

Elephants are always a funny kind of weapon

Having a big weapon on your side is a terrible advantage. Elephant is a good historical example: while they don't deal a lot of damage per se, they are terrible for enemy morale. You can only have a few, and each of them won't deal a lot of damage. But if you are on the other side, that's another topic.

Gosh, an elephant charging me! Ok, so if we all keep the formation, the elephant will crush on our spear formation. Sure, there will be casualties, but we will win. The only thing we had to do is keep our formation. Hey, what is Joe doing? he can't escape the battle, can he? Whatever, he was a coward. We can keep formation without him. But, wait, Jack is also fleeing! He was the best of us. If even he thinks we are lost... But we need to keep the formation! Oh, no, some others are also running. The formation just broke up, the odds are very bad for me. Yep, better run for my life.

Even if the elephant wouldn't do that much damage, it crushes the enemy formation, and you can now deal much more damage.

Why on earth wouldn(t you want such a weapon?

sure, the enemy also have a huge weapon. but that won't ensure you that the foot soldiers will keep the formation.

And it's because she doesn't have dragons that she wants a similar, smaller armed animal that can afraid the enemy.

So that we don't expect elephants

Golden company is well-known for their elephants. Harry Strickland is proud of them, and as it's the final season, we expect massive battles. This scene is also a way for showrunners to tell the spectators to don't expect any elephant. Sorry, all CGI budget was burned on dragons.