Spiders, in this context, are things that index the web. So you might also call them indexers. Once you index the web, there are a lot of interesting things you can do. One of the use cases is to "scrape" data. Technologies such as Search rely on indexing.
A long time ago I wrote a spider. If I ever get around to digging up that old code, here is where I might find it. But that was old school, and not really useful for anything non-trivial these days. Lots of other people are making interesting spiders that you can use. Scrapy is a Python spider. There is a visual frontend, Portia, from the folks over in Cork, Ireland at Scrapinghub.
Use Case
I want to scrape questions and answers from OKCupid. The OKC content is dynamically generated on the client-side (browser) using JavaScript. This means we are NOT dealing with a "rendered" page to scrape, but rather their application sends a bunch of JavaScript to the browser (client). The user interacts via clicks to instruct the JavaScript to perform actions and render new results. Thus we need a browser equivalent that can speak JavaScript and can load additional JavaScript for execution on the "page". Portia doesn't do this. Instead, there are a couple options to integrate with Portia or to modify the middleware[1] of Portia.
Even the OKC login page is scripted.
Splash is a JavaScript rendering service implemented in Python using Twisted and QT. Splash can be scripted. So, using Splash with Portia, we should be able to visually scrape OKC.