This will differ greatly from instance to instance. The people running lemmy.world have published some info on their infrastructure. My instance is running on a rather small VPS with 100GB storage, but I will have to rethink my solution rather soon as images and videos from my subbed communities [Edit: which are stored on outside sites] are eating around a gigabyte per day and I think this is likely to increase.
Edit: I want to clarify that I was partially wrong - Lemmy only locally caches content which is hosted on outside sites (e.g. imgur). It does not cache content that was directly uploaded to another Lemmy instance and just embeds the source media.