What are the Base Fee and Priority Fee introduced in EIP-1559?

Sure, no problem. Let's use a real-life analogy to explain this; it will make it much easier to understand.

Before EIP-1559, Ethereum's transaction fees were like a "blind auction" market. Everyone was bidding, and whoever bid highest got their transaction processed first by miners. But the problem was, you had no idea how much to bid. Bid too high, and you'd overpay significantly; bid too low, and your transaction might get stuck indefinitely.

EIP-1559 was introduced to solve this frustrating problem. It split the previously vague transaction fee into two clear components: the "Base Fee" and the "Priority Fee."

1. Base Fee - Like a Taxi's "Minimum Fare"

You can imagine the Base Fee as a taxi's "flagfall" or "minimum fare" / "base mileage fee."

This is a mandatory ticket: As long as you want to do anything on Ethereum (like transfer funds or buy an NFT), this fee is unavoidable. It's the "entry fee" that the system requires you to pay.
The price is network-wide, uniform, and transparent: This "minimum fare" isn't set by you, nor by the miners (now called validators). Instead, it's automatically calculated by the Ethereum network based on current network congestion. Just like a ride-hailing app dynamically adjusts prices during peak hours, when the network is busy and there are many transactions, this base fee will automatically increase; when the network is idle, it will automatically decrease. You can always see what the current base fee is, so you know where you stand.
This money is "burned": The most unique aspect is that the base fee you pay does not go to the miner/validator who includes your transaction. It is directly destroyed (burned) by the system and disappears forever. This is like a toll fee that goes directly to the "road system" rather than to the driver behind you. This is beneficial for Ethereum's long-term development, but for users, it's enough to know that this fee is mandatory and gets burned.

In simple terms, the Base Fee is a mandatory, burned "toll fee" set by the system based on network congestion.

2. Priority Fee - A "Tip" for the Driver

The Priority Fee is much easier to understand; it's simply a voluntary "tip" you give to the miner/validator.

This is optional, but often recommended: Just like taking a taxi, you don't have to give a tip, but if it's peak hour or you're in a hurry, giving a tip makes the driver more willing and faster to serve you. It's the same on Ethereum: this "tip" you pay goes directly into the pockets of miners/validators.
The purpose is to "jump the queue": When the network is busy, everyone pays the same "Base Fee." So why should a miner/validator process your transaction first? It depends on who gives the biggest "tip." The higher your priority fee, the more attractive your transaction becomes, and the more likely it is to be prioritized for inclusion and confirmation.
You can set the amount yourself: How much tip to give is entirely up to you. If the network isn't busy, a tiny amount (e.g., 1 Gwei) will suffice. If the network is very congested and you want your transaction to go through quickly (e.g., to snatch up a popular NFT), you might need to give a larger tip to "incentivize" the miners/validators.

In simple terms, the Priority Fee is a voluntary "tip" you pay to miners/validators to get your transaction processed faster.

To Summarize

Now, the total fee for an Ethereum transaction becomes very clear:

Your Total Transaction Fee = Base Fee (system-set toll fee) + Priority Fee (your tip to the miner)

What are the benefits of this approach?

For us ordinary users, the biggest benefit is that fees have become much more predictable. You only need to check the current Base Fee and then decide how much "tip" to give based on whether you're in a hurry. You no longer have to blindly guess the price as before, which often resulted in either overpaying unnecessarily or having your transaction stuck for ages.