TIP: EIP stands for Ethereum Improvement Proposal.
First off, EIP 1559 changes how fees work. It does this by moving from an auction system to a flat fee system based on network demand. Moving to this system should generally help lower fees, especially in times when the network is not congested.
Second, as part of this mechanism fees will be broken into two parts, and one part of those fees will be burned leading to a reduction in ETH supply and a curve on inflation. This also helps to prevent incentivizing malicious mining practices.
Also of note is that EIP 1559 makes ETH the only way to pay for transaction costs, which will help further cement ETH’s role in the Ethereum ecosystem and helps ensure only ETH will be burned during transactions.
In short, this is all a move toward fees benefiting all Etehreum holders and not just miners (consider, in February alone the network collected well over $600 million in fees), which should not only reduce gas costs but add value to the Ether ecosystem in general.
With that noted, it is no surprise that some miners were against this transition. For a full detailed breakdown, you should check out the official ETH Github EIP-1559 page.