"Regression" is a math word that means "finding a line that best fits the data".

In your example, "Linear Regression", is just one type of regression that assumes the data wants to fit a straight line.

You hear about it a lot in algorithms because they are all about taking points of data, and trying to figure out what the larger scale process that's controlling the data.

Alternatively you might have something like "exponential regression", where the data wants to fit a curve. For example, if you wanted to chart the spread of COVID-19 in the early days of the pandemic, you'd want to use exponential regression. Linear regression would work at first, but once you started projecting out a week or two you'd see that your line stopped matching the actual infection rate suddenly, and then became very wrong, very quickly.

In practice, linear regression is much, much easier to both do and understand, so it's more "popular". Exponential regression usually requires computer analysis and is more confusing to lay-people. That's just why you hear about "linear regression" more commonly.