One counterintuitive aspect of EIP-1559 is that it will not significantly lower gas prices on Ethereum. The main reason for this is that gas prices are set by supply of and demand for Ethereum block space. "Supply" can be thought of as available block space, which can be increased by raising the gas limit, shifting some transactions off chain (to L2s, for example) or by adding more capacity to the chain (with sharded execution, for example). "Demand" simply represents the amount of users that want to use Ethereum.
While 1559 allows blocks to be up to "200% full", only a small minority of blocks will end up being that large. This is because as blocks are >100% full, the minimum gas price required to be included in a block goes up. After 5 minutes of 200% full blocks, it will be up 10x. After 10 minutes, gas prices will be up 100x, and so on. This means that over a long period, the amount of "200% full" blocks will be so small as to not cause a significant increase in supply.
That being said, 1559 does improve the accuracy with which users can estimate gas prices. By having the BASE FEE as part of the block header, we can calculate the minimum price required to be included in the next block (or range for the next few blocks). This means that users will "overpay" for gas less often relative to what the "market price" for gas is.