While a detailed explanation can be obtained by googling for the ELO rating systems (and the improved Glicko systems), suffices to say that this number establishes your skill level within a given rating pool.
There are a few salient points to give you an idea of how this works:
1. Higher is better. For example, if you consider FIDE which follows the ELO rating system, the best super grandmasters in the world are rated close to 2800. Novices on this same rating scale would be around 800-1000.
So yes, the higher the number, the more skilled you are likely to be.
2. Another useful way of looking these ratings is to consider that if you played a person with a 400-500 pt+ rating difference from you (in most rating systems) , you are either expected to win 99%+ of the time (if you're the one who is higher) or win far less than 1% of the time (if you are lower). Say you are a 1600. You are expected to eat 1200 rated players for breakfast (assuming they are really 1200 rated).
3. Also, if you are playing somebody around your own "rating" score, the system expects the result to be a tied (5-5 in a best of 10 series, for example)
4. Whenever your own results are "against the system's expectation of your performance" (say you are a 1200 who wins against a 1800 player), the rating system will adjust to this "surprise" by bumping your rating up and bumping the 1800's down.
I am new to the site. I have noticed the numbers listed next to a players name. I have not yet been able to figure out ranking. Are higher numbers next to your better or worse than lower numbers?