Basically, a homelab is one or more computers in your house that you can use for a variety of IT functionality, the most common of which is self-hosting.
Self-hosting is simply a way of being your own web host (as opposed to paying someone like GoDaddy, SquareSpace, Wix, WordPress, etc.) Your personal website(s) and/or web services run on your computer, in your home or office, completely under your control, over the internet connection that you’re already paying for.
For starters, there’s the cost savings. Web hosting can easily cost $100 per year or more. The increase in your electric bill from self-hosting will be a fraction of that. Next, there’s the educational aspect; if you’re interested in IT (Information Technology), there’s almost nothing you can’t simulate (and by extension, learn) with even a modest homelab. Self-hosting a personal website or blog only scratches the surface when it comes to self-hosting. There’s a tremendous spectrum of highly beneficial services you can self-host - almost all of which will either save you money, improve the privacy, security, and/or confidentiality of your personal data, or provide you with some beneficial/convenient functionality. Here are some of the foremost examples (although this is only the tip-off the iceberg)… NextCloud, Home Assistant, PhotoPrism,
Aside from the annual cost for a domain name (mywebsite.com - around $10/year) and the cost of the electricity to run the computer (which you’ll typically run 24/7/365), the only other cost is just the computer itself. Any old PC or laptop you have laying around will do but you could also buy an old laptop, netbook, thin client, or mini PC (i.e. on eBay) for $50 or less.