I really just want to grasp how a bitcoin actually is something of value? and how a string of characters equate into something that is worth dollars?
Proof of work plus utility, and scarcity.
The Bitcoin mining process is what creates new coins in the Bitcoin economy. To add a new block to the network the miner must produce a hash below a specific target. The only way this can be done is through trial-and-error (bruteforce) so miners are constantly competing to produce as many of these hashes per second as possible so that they earn the newly created bitcoins.
This competition requires hardware and electricity, both which cost money. This is the Proof of Work (POW), the only way to create new blocks and thereby new bitcoins is by spending money on the mining process. This is also where the scarcity part comes in. Today, every block created produces 12.5 new bitcoins. Every 210,000 blocks (~ 4 years) this reward is cut in half thereby constricting the supply. We've already had two halving events so far. It started at 50 new bitcoin per block.
Lastly utility gives it value. Bitcoins are useful. They can be used to transfer value across the globe almost instantly, for very little cost, and without censorship. Whether it's used for international remittance or gambling doesn't matter - bitcoins have utility.
So it's not just random string of characters. What appears to be random strings actually represent and mean something. They can be validated by others that can prove that this string of characters represents the money and energy spent creating a valid block.
Long ago, Aristotle defined 5 properties that he felt were needed for something to be used as a currency:
- Intrinsic value
An additional property that we have come to agree on is Scarcity.
Throughout history, humans have created many currencies that lack one or more of these properties. For example, the island of Yap used extremely non-portable, non-divisible Rai Stones. Currently, most nations use fiat currencies like US Dollars, that lack any intrinsic value.
Bitcoin excels at all of these properties, except intrinsic value. In terms of intrinsic value, this puts it at the same level as USD...not below it.
However, another property of currency to consider is legal tender. This means that a currency is acceptable as payment for taxes. USD is legal tender in the US, but bitcoin is not. If you get paid and buy all your goods with bitcoin, you will still need to convert into USD to pay US taxes (if that's something you need to do).
If you take all 7 of these properties (including scarcity and legal tender) into account, bitcoin beats USD in 5 of them, ties in 1 of them (intrinsic value), and loses to 1 of them (legal tender). All in all, that makes it a pretty good currency.
So there's a simple answer to your question about how a data stored on a p2p network can be worth US dollars: dollars aren't worth as much as you think they are.
Well, the technical answer was given correctly above (I think), however the valuation and the acceptance of bitcoin lays somewhere beneath these technicalities. The most probable reasons that a virtual "money" like this could work are greed (the price will go up further), anonymous trust (others will accept it as a money, not just you) and so on and on, but you must look for some sort of greed as a motive.