I still don't understand how bitcoin works and how people just "mine" them and can use them.
me neither. I'm just curious bystander and watching the firework. I do wish I had learned and mined some when people here were doing it. I have no interest in jumping on the bandwagon now. I just thought it was some stupid fad and waste of electricity like that searching for alien life project. I remember lot of people arguing and talking about bitcoin when it first broke $1,000 and crashed and burned. Everyone laughed and said I told you so and thought that was it. But this time, no one is talking about it. It's almost like people don't care. Or maybe they finally accept it as real now. Whatever the reason, I don't see the recent rise talked about much. Which is why this climb could have further legs.
It helps to understand how cryptography works first. A few years ago Steve Gibson did a good basics on how it works.
Here's how I understand it, though as a general layperson without having a computer science or heavy math background it's going to be simplistic and probably flawed:
The essence of Bitcoin and other cryptocurrencies are that most of them are a Proof-of-Work system and a blockchain. Proof-of-Work (PoW - there's also Proof-of-Stake or PoS algorithms used by some cryptocurrencies) addresses a key general problem mathematically: proving that you have done something ("work") by solving or decrypting a cryptographic hash (algorithmically generated). Mining is putting your CPU (not used commonly anymore, as GPUs have more parallel processing power for most cryptocurrencies, and purpose-built ASICs even more so) to work continuously in order to solve these hashes.
The hashes aren't just a random collection, though, ultimately what your computer is looking for when mining is the solution for the current "block". A block is a transaction record, a little like pages or a section of a ledger. If your computer finds that block solution before someone else's does, you get the reward for that block (a certain amount of Bitcoin or whatever currency you are mining).
For most mature cryptocurrencies these days, though, because of built-in increasing difficulty (mining power needed to find a block goes up each "round") it's more effective to be part of a mining "pool", where you share the reward from finding/solving a block. Otherwise you'll go through dry spells of days, weeks, or longer if you mine solo.
All the blocks together form a complete ledger of all transactions for that particular cryptocurrency in what's called a (or the) blockchain. The blockchain data isn't stored on a single server somewhere centrally, but instead it is split into chunks and distributed (using the same type of technology behind Bittorrent) and stored on every computer* that runs a "wallet", which is used also to receive and send that cryptocurrency. Each cryptocurrency has it's own blockchain, and the constant encryption/decryption verification process and distribution mechanism of the blockchain is what makes cryptocurrencies attractive, as it's a decentralized network that doesn't rely on a person or group of people to maintain the integrity of the system.
What's driving increased prices of Bitcoin and Ethereum are scarcity and speculation. "Scarcity" sounds funny because it's a digital currency, but there's a fixed limit (21 million BTC total in the case of Bitcoin) that can be mined, and the increasing difficulty means it takes more and more computing power to obtain a single unit of currency or even a fractional amount.
Speculation is driven mostly driven by confidence and news. The resurgence of cryptocurrencies right now is more centered around Ethereum, in my opinion, but that's still a tide that raises all boats, including Bitcoin which is still the de facto cryptocurrency and often used as an intermediate currency to traditional fiat currency. There are number of interesting projects around blockchain technology, big financial institutions are starting to use them for their backend interbanking ledger systems, the IMF held meetings and presentations on cryptocurrencies, cloud providers like Microsoft and IBM are invested in them, IoT device companies... all sorts of activity going on right now.
Sure, some of it is hype and leading to a bubble, but that's really how human development operates, in bursts of interest, disappointment, and then renewal of interest. Knowing when to get in and when to get out - if you are interested in just the financial side - is as difficult as anything else. Bitcoin kr Ethereum could be worthless a year from now, but that's just as true of many "real" currencies. The risks and rewards are higher for sure with cryptocurrencies right now as it's still a nascent technology and field.
* there are light wallets that don't store the full blockchain data, because blockchains tend to run GBs of data and grow over time