Zero interest rates meant that speculative investing (for the purpose of selling later for more money, not for any dividends a company might pay from any profits) with lent money (aka leveraged investment) was pretty much a risk free proposition since loans with zeto interest rates cost no money to maintain. (You and me don't have easy access to loans for investing from the money markets but the kind of investor we're talking here does)

Interest rates go up and that lent money now has significant costs associated so investing with lent money (and nowadays that is most of investing done at professional levels) now has to produce enough returns to pay the interest on the loans hence all the pressure for companies to generate profits.

(Note that money from the money markets is typically on much shorter terms - and loans usually are rolled-over into new loans on maturity - than consumer loans, so interest rates on those respond much faster to changing base interest rates than for consumer loans)

(Also the companies themselves also have loans that they now need to pay interest on, which adds a more direct pressure to start having a positive cashflow)

As for central banks raising base interest rates to combat inflation, the idea is to literally make people have less money available (I kid you not: people are supposed to be made poorer) so that they don't buy as much, and that reduction in Demand will cause prices to fall.

Edit: I was thinking about this and realised I had moved the ??? around but not clarified it all. Specifically, how do we go from "speculative investors having less cost-free money" to "companies which have eternally been in 'investment phase' (i.e. losing money whilst promising they'll one day be the greatest thing since sliced bread) being forced into trying to actually have profits". Well, for the stock price not to fall too much (which might lead to a rush-to-the-exits, a feeback-cycle were the more money that exits the less the worth of the stock, so the more money exits) and as speculative investors are fewer and/or have less money to invest, they have to appeal to more traditional investors, the kind that judges a company's worth by their (stock-)Price-to-Earnings ratios (which, by the way, is a ratio that the smaller it is the more appealing a stock is to buy), so to have good P/E ratios without the Price side going down, the Earnings (basically Profit) side has to go up, hence the need to generate some profit (notice that the P/E of a company without profits is INFINITY), which is what pushed them to try and come up with profit NOW to hold their valuations and sometimes even at the cost of future profitability.

This also links with another element I forgot to mention early: the "climb up the yield scale". In simple terms (as much as possible) - most of the money out there not in the hands of States is owned by two kinds of entities - Pension Funds and the Rich (which, given the extremelly uneven distribution of money actually own more money than everybody else combined) - and they're not just putting it on a bank and getting Savings Account interest on it, they're looking for ways to make money from money. Now, back in 2010 when Central Banks "rescued" the Economy through their Zero Interest Rates Policy, that money which was mainly parked in the safest of investments (Treasuries, Investment Grade Corporate Bonds) started getting puny amounts of interest, eventually even losing value (remember how the Treasuries of many countries started having a negative yield - i.e. you paid those countries money to hold your money?!) so they started going up into riskier and riskier asset classes seeking a higher yield (i.e. higher returns on their investments), up and up into Junk Bonds, Stocks, Realestate, Tech Stocks, Startups and even really exotic asset classes like digital "coins" (I very much doubt there would ever have been a Bitcoin mania without all that money seeking yield due to ZIRP), all of which is the "climb up the yield scale".

Now the "climb up the yield scale" sounds like the opposite of what would make companies which are mainly speculative investments try to make profits because it is exactly that: the rise of baseline interest rates reverses that trend - it makes safe financial assets more appealing (holding Treasuries now actually pays interest, not cost interest, and just up the risk scale investment grade corporate bonds also pay more) which is pulling all that money down (remember, rich people and pension funds: they're usually quite averse to losing money, i.e. more risk averse that, say, Investment Banks, especially old-wealth) and out from the higher-risk and more speculative investment classes, noteably Startups (and further down Tech Stocks and even Realestate). This again puts pressure on companies which were so far profitless to produce profits: it makes them look safer hence retain some of the investment which had before climbed the yield scale when the safest of investments had ridiculously low (even negative) returns.

There are actually yet more ways through which higher interest rates feed into speculative companies trying to put on a pretty face by actually having profits, but this post is more than long enough already ;)