As the above poster said, it really depends on the job you're applying for. When in doubt, ask HR or anyone you can get in contact with, but here are some general guidelines:
A lot of concept art is still done the traditional way, but you'll need to know how to scan it in and optimize it by use of Levels and Brightness/Contrast, possibly Color Balance when applicable. Many studios will expect you to know how to use a tablet, so you should look into buying a Wacom if this is your preferred path. And honestly, if you like creating digital art a Wacom will be the single best investment you'll make in terms of art supplies. Also know how to use and create custom brushes, keyboard shortcuts used in sketching and painting, basic techniques for layers, digital sketching, and digital coloring.
Some studios have their texture artists do everything from scratch, but most recognize the time this takes and encourage image manipulation. Learn where to find stock photos and how to judge their quality. Learn and love the clone stamp and healing brush as they are the single most invaluable tools in your arsenal. Learn how to use offset to make seamless textures. Learn how to use (and not overuse!) dodge and burn. Learn all of the image adjustment and optimization tools including levels, brightness/contrast, color balance, etc. Learn all the shortcuts. All of them. Have extensive knowledge of layers and layer masks. If you're going to be painting textures by hand learn how to use and make custom brushes because they will save you time and make your work higher quality.
Technical art is an odd sort of discipline because it mostly means you're going to be working more on implementation and speaking in programmer code than doing art, but in some places a technical artist makes special effects. If this is what you're after, master layers, layer masks, layer styles, and layer effects. I've noticed most special effects made in PS are made using layer effects rather than filters, but it's probably a good idea to see what filters do what and learn how to overcome the 'amateur' flag they raise. Install filters and plugins from the web such as Eye Candy. Learn and love custom brushes. Learn and love image adjustment tools. Become familiar with all of the shortcuts. Don't be afraid to go bold.