BTC/USD price changes approximately the same way over many exchanges at the same time, how?
To be more specific about the "arbitrage strategies" in Tanmay's answer:

Suppose there were a difference in price between two exchanges: at A the price is $10,000 and at B it is $10,100.  Then, in principle, someone could turn a quick and risk-free(*) profit by buying coins on A, transferring them to B, and selling them for the higher price.  This is called arbitrage.  As they do so, it will tend to drive up prices on A: the people who were offering coins for sale at $10,000 on A are having their offers accepted.  Eventually those offers will all be gone, and people who want to buy will have to take the next-best offer, which will be at a higher price.  Similarly, this strategy will also tend to drive down prices on B.

Arbitrage thus tends to make prices on different exchanges converge towards equilibrium.  And it can happen very fast, so significant differences in price, even if they should occur, don't tend to last very long.  Most of the time you see prices that are close together.

I have left out some details: for instance, the arbitrage strategy will incur transaction and trading costs, and it is not completely risk-free since prices could change in between trades.  This is part of why you don't see prices looking exactly the same at all times.  But the principle applies, and it's a fundamental principle in the study of finance.