Web designer is a blanket title that covers a lot of tasks and skills that cater to the web as a medium. Depending on the Web Designer’s position and skills, it can encompass:
Design of websites, web apps, native apps and really any platform intended to be displayed on the web.
Programs like photoshop or sketch are sometimes used for graphic design and layout.
Designing/strategic planning on user experience in regards to the functions and sitemap.
Designing user interface elements which are commonly used elements like buttons, alerts and more that get used across a web property like a website, webapp so on.
Building new web sites utilizing at least front end languages such as HTML/CSS/JS and tools related to that like CSS preprocessors, jQuery and much more.
Maintaining existing websites using CMS tools the web property may be built on or the aforementioned front end languages.
Designing and building marketing campaigns which will be displayed on web properties.
Keeping up with innovations, trends and changes, of which there are many and often.
By extension a web designer may also find themselves doing:
Light to heavy backend development with server side languages.
Email marketing design.
Social media channel artwork like cover images, youtube channel pages and so on.
General marketing consulting to help clients understand and utilize things like analytics and optimizing for search engines.
It really depends greatly on the amount of skills a web designer has and is willing to use. It certainly can be a position that keeps you on your toes and challenges you at every corner. I feel like I’ve done everything listed above and then some. Things like copywriting, speaking, animation, illustration and print design can become part of your repitoire if you’re so inclined too. Once clients generally find out you can do one thing it opens the door to others.