You work in an office full of people. Everyone sits at a round table for meetings and brainstorms as a team. Are you all equal? Probably not. If you didn't all join the company at the same time, if you don't all earn the same amount, and if you don't all have the same job description, then some employees have seniority over others. If you're not familiar with the concept of job seniority read one definition here.
Job seniority is what you have when you are more valuable to the company than someone else. Job seniority sometimes results directly from the hiring process - the shop floor managers are automatically in charge of the robotic arms - and sometimes it comes about by having been employed at the company longer than other employees or having more training and education than other employees. Either way, certain privileges are associated with having job seniority.
In companies where employees are unionized, privileges are awarded by job seniority, which is earned through experience managing or teaching classes or whatever it is that the union's employees do. In a unionized company, the more senior employees have first pick of shifts or work schedules, more choice over what tasks are assigned to them, and more job security if there are going to be layoffs or transfers within the company. Airline pilots, for example, choose their aircraft and routes based on their rank in the union. The office manager at a dental practice might give the more senior staff first pick of days or weekends off each month. At a company with 5 different office locations open six days a week, it's a challenge for the person in charge of schedules to meet everyone individual's requests, so the ultimate trump card for getting Saturdays off becomes seniority.
Employees who have the least seniority are usually assigned the work that no one else wants to do and are the first to go without work when times get tough. Teachers, for example, spend the first few years of their career substituting for more senior teachers who are off sick or who need help chaperoning their students to art galleries. When positions open up, they go to teachers who have been around longest, not necessarily to the teachers who are the most qualified.
So how can you get job seniority? You can minimize the amount of job hopping you do and stick with one company. The longer you stay, the more senior you become. However, in some companies there is a limit to how senior you can be without extra training or education, so if you work in a office, you may want to take a course in management to make you a more attractive prospect to the people who are handing out promotions.