Problem you're trying to solve: "I need to create a report based on a certain period of time (like 'this month, or last quarter'). I don't want to use specific dates because I'd like to be able to reference the same report repeatedly without needing to constantly update it"
Either select time frames from a dropdown OR type them in the text of the filter when leveraging a Date field.
At the top of each Salesforce report, you'll see a standard Date filter. You can update the field referenced and use the dropdown to select a relative date range. There are many options here.. but not all.
If you need to apply a relative date filter that is not available in the dropdown options (ex. '6 weeks ago', 'Last 6 months', etc.), select 'All time', add the date filter as an additional filter, and apply the desired filter.
Add a Date field as a filter. (If you're in Lightning, click 'Relative')
Then type in your relative date range and click 'Ok' to apply
Source: Salesforce documentation, Relative Date Filter Reference