How tubes influence sound

Your question is quite broad-ranging, and there is really no simple one-fits-all answer. There are different circuit designs using tubes, different tubes and different utilization of the tubes. Some designers only use tubes in a portion of the circuit. A sort of historic answer is that tubes sound better in the midrange than SS and are not as extended at the frequency extremes. That is not necessarily fully true. I have found the most apparent differences to be in dimensionality/soundstaging, tonality, and harmonics or decay of notes. A good tube implementation will beat most SS units in those areas. These benefits may be more pronounced in the midrange, resulting in the reputation tubes have for better midrange. My current tube preamp improves on any SS unit I have heard in those areas, and is reasonably extended at both frequency extremes, provides good bass punch, and just simply sounds more real on vocals. Most of the tube preamps I have heard share similar characteristics, but like SS units some are better at certain things than others. It seems where they struggle the most in comparison is in the bass, where they do not always provide as much extension, definition and punch. You need to listen for yourself.