Work experience is a commonly used term that can mean different things to different people.
Generally it means spending a period of time in a place of work observing what happens and undertaking any duties that may be appropriate. It is not normally paid, although sometimes companies will re-imburse your expenses, and you should not be replacing a paid employee.
Many courses offer work placements as part of your studies. If this is the case it is more likely that you will undertake a role that gives you experience or training that is directly relevant to your studies. You should also expect to have some opportunity to apply skills and knowledge you have learnt in your course directly.
Even if your studies do not include a work placement, you may like to consider organising work experience yourself, or through your college. While most students will have some experience of work, it may be worth gaining experience in a specific area you are interested in, or if you're not sure what you want to do and want some idea of what's involved with a certain job.
In certain industries work experience is considered very important. For example, many employers in the media will assume you have done some related work experience. They are also used to being asked to offer work experience and many companies in this industry have work experience schemes. Other industries, like health care, are more likely to provide direct experience to students as part of continued study, and may be less able to offer work experience to students on an ad hoc basis. Talk to your college's careers advisor for more help.
Precisely what is involved will vary depending on the organisation, what member of staff or department you are shadowing, and the nature of the work they do. However, it is also up to you. The more enthusiastic and willing to learn you are, the more you will get out of work experience.