The Market Capitalisation, or "Market Cap" of a company with shares is a very simple idea.
You take the previous price of the last share that was traded, and multiply it by the number of outstanding shares. The prices are simply a result of the "Bid-Ask Spread"
So let's say a share just changed hands for $120. And let's say there are 400,000 outstanding shares. This "values" the company at 120 X 400,000 = $48m.
Is this realistic?
Not really no, because the chances of actually being able to purchase all the shares at this price are basically zero.
The reason for this is again the bid-ask spread. You will not find all the current owners of the share willing to sell at the previous market price. Many of them will want more money for that share. So as you start to purchase the available stocks at the current price, you will run out of sellers at that price.
Your only option then is to put in higher bids to persuade the next tranche of sellers to part ways with their shares. This then moves the stock price upwards. This movement might convince other sellers that they should hold out for more money, and so can actually influence the bid-ask spread against the person trying to buy the company.
For a real-world example of this you only have to look at Elon Musk's purchase of the company Twitter. The more shares he bought the higher the price went, meaning the total he paid for the company was much larger than the original market cap of when he started acquiring shares.