Unfortunately, "senior", like so many other words that imply better somehow, has gotten diluted. If you're really cynical, then "senior" means about as much as "deluxe", "grande", and "turbo".
To answer the question more directly, as a job seeker you have the right to expect "senior" to mean:
- More advanced than whatever the entry level version of the job is. There must be at least one, preferably a few levels below a senior person. These are not necessarily managerial levels, but levels of responsibility and higher level decision making authority. For example a senior engineer probably wouldn't be the political boss (wouldn't be doing salary reviews, etc) of junior engineers, but would have higher level authority over a design.
- Expected to help grow junior people. Part of the responsibility is not only to watch that junior people are doing the right job or a good job, but to help them learn their jobs. Not only should you be using a fraction of your time to deliberately mentor junior people, but also be available as a go-to resource for those junior people.
- Be included in some higher level discussions regarding overall direction, not just handed well-defined tasks others have already decided need to be done.
- Take a fraction of your time to look around, think a few levels higher, and possibly find things that could be done differently. This is the opposite of just doing what your told and not asking any questions.
How senior (according to the above points) senior really is in any one organization can vary. Partially due to the dilution of the term "senior", there may be other levels. For example, nowadays a "principal engineer" is a more senior "senior engineer".
As with any term like this, it's a rough guide at best. You need to look carefully at the text of any job description, and don't be afraid to ask questions if what you're interviewing for doesn't seem to match the writeup for the job on the web site.