What Happens If I Copy Some Text From Another Website?

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For SEO, this is not good for your website. Google will have an excellent record of who originally prepared that text for their own website and they will then do quick analysis on the new text on your site and see that you copied it.

The optimisation that you're trying to do for that page and that keyword is then in vain as google will not give you a good SERP ranking for copied text. Equally, it is a bad mark against your domain and google will log that in case you try that text-copying again or any other seo technique prohibited by Google.
If you already have some 'bad marks' against your domain  e.g. for buying backlinks, hiding seo-optimised text, showing different text to google and web visitors ... then you could get removed from the Google index system and not appear for any searches.

Google Can See All Web Content

In general, prepare your own text and use some piece of text as inspiration and direction but don't copy any text - google will see it. On the same topic, google can also see if you are grabbing images off the net and reusing them .... so it is also a good idea to slightly resize images if you have bought stock photos or maybe take your own images.

All these images have a digital signature and to reuse an image is not what google wants - google wants original content and images.
If you are concerned about a piece of text ... whether you wrote it or whether you copied it ... put it in quotes e.g. "this text better be original or google won't like it " and put it and the quotes into google and you'll see if that piece of text is attributed to some other web site.

You can experiment with this but you will need to use a good few words because if your search is for just a few words then of course you will see results coming back from google.