The horizontal asymptote is basically a horizontal line which is the closest to the x-axis in a coordinate plane.

For example take the exponential function y = 2^{x}

First prepare a table for the same by plugging in x = 0 we get y = 2^{0} = 1

x = 1 we get y = 2^{1} = 2 etc.

Plotting these points on the coordinate plane we get

Now join these points to get the graph of the given exponential function

As you can notice that as x value decreases the graph comes closer to the x-axis. As we know the x-axis is horizontal and on the x-axis we have y = 0 So, at y = -2 we have a horizontal asymptote of the function y = 2^{x} since this is the closest point where the graph touches the x-axis.

More on horizontal asymptotes:

https://magoosh.com/hs/ap-calculus/2017/find-horizontal-asymptotes/

Further skills you may want to recall:

What is an exponential function

https://www.mathsisfun.com/sets/function-exponential.html