If you have problems, you should probably add flux (make sure to extract fumes if soldering with flux for a while). Some say there is never enough flux.
Depends on brand. And my head always hurts after inhaling them for more than a minute without a fume extractor. (I just use a PC fan and some old who-knows-what HEPA-like filter discarded from ventilation equipment. For quick jobs, I hold my breath and/or move out of the way.)
What it looks like: You shat all over the board.
What it smells like: Nasty chemicals but only when hot.
What it does: it helps distribute heat, and causes the solder to be less viscuous and stick to metals readily.
What it feels like to start using it: Wow, it's like I just gained one year of soldering experience!
What it feels like to remove it from the board after soldering: Aargh... I swear, one more board and I go buy an ultrasonic cleaner. (Some brands are easier but I usually need to employ a spudger, brush, then alcohol annd Q-tip)
Note that some solder comes with a core that contains flux or some similar substance of that effect.
It removes the oxide layer from existing surfaces so the solder sticks and flows better
It increases surface tension of the liquid solder so you get a nice round shape and no whiskers and less bridges
It helps distribute the heat a bit. It works a little bit like thermal paste, especially when the contact area between the tip and the pad/component is very small.
Generally, flux is your friend and soldering without flux is terrible.