The binomial distribution is symmetric when p = 0.5. It has a negative skew when p is larger than 0.5 and a positive skew when p is smaller than 0.5. The larger the value of N, the less the skew for a given value of p (other than 0.5 where there is no skew for any sample size).
The mean of the binomial distribution is equal to Np. Therefore, the larger the number of trials the larger the expected number of successes.
The spread of the binomial distribution is greatest when p = 0.5. The farther p is from 0.5, the smaller the spread.