All you really need to play the game is pen, paper and some dice. However, with a laptop or smartphone you might even need less as you can utilize digital dice for rolling and an online character sheet. While this is the bare minimum, there are those who are much more invested and involved with D&D opting to purchase supplementary material.
Dice Goblins: Believe it or not, you only really need one set of dice for D&D. However, this doesn't stop some players from buying and/or collecting new sets of dice. They'll have more dice than they will ever know what to do with, but as long as people keep making incredible looking dice, they will keep buying more and more. I will admit that even as someone who rolls my dice digitally, I have bought into the culture of what we call dice goblins and purchased an ungodly amount of dice that I found to be extremely appealing visually.
Dice Towers: Believe it or not, purchasing way to many dice sets is relatively tame when it comes to higher levels of investment in D&D. Sometimes people will purchase dice towers to roll their dice down as a fancy way to obtain the results of your roll.
Internet: You can also find countless resources online in the form of digital tools for your D&D games. In most cases, the games you will be playing will be at home and between friends. Meaning that you are free to use any and all resources you find online. That most commonly includes artwork you find on Google and background music from YouTube. You're playing with friends at, not broadcasting it for commercial purposes. There's no need to worry about getting sued for copyright infringement.
Beyond: Buying any other supplementary materials beyond just dice and dice towers usually falls into a level of investment far beyond that of your typical player. This can include the purchasing the purchase of maps and miniatures to play upon them to represent your characters in a given location. Going further, others have painstakingly created 3D maps for their games and even invested in a digital screen being incopoorated into their tables for a large battlemap that can be changed seemlessly.