The Owner is the user that currently is responsible for the issue. Workflow rules can transfer ownership of an issue automatically, on changes in status. Like for example, transfering an issue/task back to the reporter for testing after work has been done on it.
If you want to keep track of the user that is doing the actual work on an issue, then you may need to use an extra "Responsible user" field for this (developer/implementor/executor).
For example you might have one user reporting an issue, or creating it by entering the requirements, then one user responsible for doing the actual work on it and a third for testing/verifying it and so on. In this case it is useful to keep track of the responsible user to be able to create a workflow for this based on statuses.
In simpler workflows you might not need the responsible user field, and in that case it is easy to remove. You can do this in (account) "Settings" --> "Issue fields" --> choose "Default", or another issue field configuration --> uncheck the "Use" checkbox for the "Responsible user" field and click save.
For more information about the workflow, see here.