A z-score says how many standard deviations a value sits above or below the mean: z = (x - mean) / standard deviation. A score of 85 on a test with mean 70 and standard deviation 10 gives z = 1.5, which is better than about 93.3% of results if the scores follow a normal (bell-curve) distribution. Percentile comes from the standard normal cumulative distribution, the share of values below z. The two-tailed p is the chance of landing at least this far from the mean in either direction.
Zero is exactly average. Roughly 68% of values fall within z = -1 to 1, 95% within -2 to 2 and 99.7% within -3 to 3, so a z-score beyond 2 or below -2 is unusual.
The z-score itself works for any data, but the percentile and p-value are only accurate if the data are roughly normally distributed.
Use the standard deviation calculator on your data set, which gives both.
See also: standard deviation calculator · average calculator · percentage calculator