"Clone depth" is a feature of git to reduce server load: Instead of cloning the complete repository (as usually done with git), using clone depth just clones the last clone-depth-number revisions of your repository.
In literature this is also called "shallow clone"
For example See here: Git Beyond the Basics: Using shallow clones
Just to extend on what Johannes said: Bitbucket Pipelines uses a "shallow clone" by default to clone your repository into the build environment. If you have a large repository, a shallow clone will decrease the amount of time it takes for you repository to be cloned into the build environment. Typically you will only need to build/test recent commits, so there is no need to get the older ones.
Some deployment tools require the entire repository history in order to work. So the full clone feature exists to support these tools. There were also some issues with old tags not being in the clone (as they were more than 50 commits behind HEAD). So using a full clone (or a larger clone depth) means you can see all the tags in your repository.
If you don't hit any issues at the moment in regards to cloning, it's likely you can stick with the default.
depth: 5 # or some other number of commits. You can also configure 'full' if you need the entire commit history.
... # standard pipelines stuff from here
Look here for more details: https://confluence.atlassian.com/bitbucket/configure-bitbucket-pipelines-yml-792298910.html?_ga=2.243827725.922211975.1534723907-825437565.1515570924#Configurebitbucket-pipelines.yml-ci_cloneclone
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