Since Mastodon is federated, running your own instance is largely transparent to most Mastodon and Fediverse users. You're simply another profile on another instance. Content will federate.
What operating your own server does provide is:
1. Control over your own services. Notably, over what other instances can federate to it --- Adam Davidson (ex of New Yorker, NYT, NPR, etc.) discovered this yesterday: <https://journa.host/@adamdavidson/109297137123981377>. But also moderation and content policies as well as operational and provisioning decisions.
2. An additional indicia of who you really are. BigCo@FlippantMastodonInstance.Whatevs might or might not indicate strong branding. BigCo@BigCo.TLD (especially where BigCo.TLD is already strongly established) is stronger branding.
3. For those not yet using Mastodon, the self-hosted server will be a single point at which content can be viewed. Note that this is marked distinction from the practice of the past decade or so of relying on social media services which were effectively walled gardens: Twitter, Facebook, TikTok, Instagram, and the like.
4. DMs are visible to an instance's admin. Self-hosting means that the organisation would control that particular exposure as well.
Much as BigCo would be expected to operate or present its own website or blog, and frequently its own email server (or at least domains pointed at hosted services), so too with self-hosted Mastodon.