How/why does increasing the number of jobs increase inflation?
When the economy gets towards the theoretical Full Employment level (not the same as 0% unemployment), and employers still need more employees, then according to the law of supply and demand they should start to bid up wages so as to poach employees from other companies.
Practically, I find that dubious.
Why would rising inflation (and interest rates, I understand that interest rates are intentionally raised to combat inflation) cause people to sell off their stocks?
As @AndrewLazarus mentioned, the stock market has been the best place to get yields, since interest rates have been so low.
With rising interest rates, you can (theoretically) get good returns without as much risk. Thus, you sell off now while the market is high, so as to have cash available when things shake out.
I think it's the herd of sheep mentality, though, combined with algorithmic trading that kicks in when certain conditions are reached.
What does this mean for me on a personal finance level? I personally don't actively invest in stocks at present,
Not much. Maybe you'll get a bigger than normal raise.
but do have some savings in the bank,
If it's in an online bank, you'll have notice increasing rates over the past couple of months.
but I'm sure other readers would be interested in a holistic answer covering stocks/bonds/cash/employment/etc.
There are too many computer algorithms, and so many people automatically shoveling money into the stock market (401k, etc) for me to even dream of a holistic answer. Anyone who gives you one is guaranteed to be wrong.