Not just a computer... equipment could be anything needed in the course of developing -- or testing -- the software. I'm thinking of something like a warehouse management tool and you interfaced with a barcode reader or something like that.

You're also legally bound not to compete with your company. You can't work for Google and build a search engine "on your own time". you can't work for Nintendo and make a game on the side.

What it means to compete will be decided by judges and lawyers in the gray areas but probably not hard to imagine clearly problem areas and likely not problem areas. If you want to know for sure, ask a lawyer and get a contract/letter from your employer to clarify.