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The two main update methods are: Weekly emails and Jira update.
Weekly emails was the style most teams used in the past, but they're now redundant with Jira updates, so we strongly recommend you to use Jira directly.
Here are the explanation of both, however, so you can interpret other people's reports, if they still come in that fashion.
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However, plans not always work as weeks pass, and it's ok to plan one thing on the previous week and do something different this one. For that reason, you don'y have to explain every plan that didn't work in this section, only the major and uncommon occurrences.
Jira update
Now that we're all using Jira Kanban boards, we can see our progress as it happens. Adding comments directly to the tasks, moving them across the board and creating new tasks on the fly is the best way to report your progress without adding bureaucracy to the process.
Furthermore, project managers and tech leads scan the Jira updates (using weekly and monthly filters based on changes to cards) to know what happened. These updates are scanned by hand and scripts, and they update other project management structures, "Health Check" and "Engineering Update" reports every month.
But for that to work, the right cards need to be updated as you progress, with comments and changes to the workflow (status, priority, sub-tasks). If engineers don't update the cards, tech leads and project managers have no way to know what has been done.