Screen sharing: Used mostly in corporate environments to let tech support workers see or control your screen, and perhaps perform repairs/updates. Windows and Linux computers can also use it to control your Mac's screen via VNC. Not heard of VNC, not in a corporate environment, and never access your Mac remotely? Ensure it's turned off.
File sharing: Lets other computers on the network access your computer's file system, including Linux and Windows computers (technically speaking it enables Windows File Sharing (SMB), Apple Filing Protocol (AFP), and Network File Service (NFS)). Notably, the file sharing system is also used by the Back To My Mac service, which is part of iCloud and allows you to access your Mac's files from another Mac via the Internet (although it has absolutely nothing to do with iCloud Drive, which performs a similar function). If you're not sharing files across the network, and not using Back To My Mac, then this option should be switched off.
Printer sharing: Shares any printer connected to your Mac with other computers on the network, again including PCs. Should be turned off if you're not sharing your printer, or if you don't even have a printer attached to your Mac.
Remote login: Allows connection to your Mac via SSH/SFTP, and mostly used by techies to work at the command-line when away from their Macs. Should be turned off if that description doesn't apply to you - and we're pretty sure it won't!
Remove management: Used in the corporate environment to let administrators access your Mac to do things like perform upgrades, or make fixes. Should be turned off in all other circumstances.
Remote Apple Events: One of Apple's many Good Ideas From Long Ago, this lets one Mac control another to print, or do just about anything, in fact, thanks to tie-ins with AppleScript, at one point a cool joke amongst Mac fans was to use Remote Apple Events to make another Mac speak, via speech synthesis. The user of that Mac would be scared half to death when his computer seemingly came to life. However, if you need Remote Apple Events in our modern age then you'll already know all about it. The rest of us can switch it off without worry.
Internet sharing: Lets one Mac share a Net connection with other Macs. This was created in the days of dial-up Internet. It's extremely unlikely to be used now that broadband, Wi-Fi routers and home networking are the norm, so should be switched off.
Bluetooth sharing: Lets a Mac send and receive files to and from another Bluetooth-enabled device, such as a mobile phone. iPhones and iPads can't share files this way, so you're only likely to use it if you've an Android phone. You'll find guides online telling you how to do this. However, in all other situations this option should be turned off.
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