Each time you redirect your output, it creates that output file anew. What if you want to redirect output a second (or third, or …) time, and don’t want to clobber the previous output?
The double greater-than sign (>>) is a bash redirector that means append the output:
$ ls > /tmp/ls.out
$ cd ../elsewhere
$ ls >> /tmp/ls.out
$ cd ../anotherdir
$ ls >> /tmp.ls.out
The first line includes a redirect that removes the file if it exists and starts with a clean (empty) file, filling it with the output from the ls command.
The second and third invocations of ls use the double greater than sign (>>) to indicate appending to, rather than replacing, the output file.