Things change in price over time. For example, a movie ticket in 1955 might cost \$.50, and a movie ticket today costs about \$10, 2000% as expensive in 2019 as in 1955. (source)
These are nominal prices. That is, what is the number of dollars I need to pay for a movie ticket?
However, these nominal prices might go up for two reasons. It could be that the item is getting more valuable. Or it could be that the dollar is getting less valuable. In other words:
(1) One is that the relative price of movie tickets might be going up. That is, movie tickets are getting more expensive relative to other goods. For example, imagine a loaf of bread also cost \$.50 in 1955, but cost \$5 today (I'm making these numbers up). In 1955, you'd have to give up one loaf of bread to have enough money to buy a movie ticket. But today, you'd have to give up two loaves of bread to buy a movie ticket. So movie tickets have gotten more expensive relative to bread.
(2) Another reason that movie tickets might get more expensive is because everything gets more expensive together. In other words, the value of the dollar drops. In 1955, you could trade a single dollar for two movie tickets, or for two loaves of bread. Today, you can't trade a single dollar for even one of either. In other words, a dollar today is less valuable than a dollar in 1955.
This second reason, where the value of the dollar drops, is called inflation.
Adjusting for inflation is a process of getting rid of any price changes that happen for reason (2). This is done by calculating (usually using something called the Consumer Price Index) what the prices of things would be if the dollar still had the same value that it did in a different year - if inflation had not occurred (we've adjusted for inflation).
According to the US Inflation Calculator, a single dollar in 1955 is 855.8% as valuable as a single dollar in 2019.
So that 2000% comparison of movie ticket prices we had before? That actually represents that movie tickets are 2000/855.8 = 2.34 (234%) as expensive in 2019 as in 1955 - a 134% increase in relative price. The rest of the nominal price increase is because the dollar itself got weaker.