A standard normal table, also called the unit normal table or Z table, is a mathematical table for the values of Φ, which are the values of the cumulative distribution function of the normal distribution. It is used to find the probability that a statistic is observed below, above, or between values on the standard normal distribution, and by extension, any normal distribution. Since probability tables cannot be printed for every normal distribution, as there are an infinite variety of normal distributions, it is common practice to convert a normal to a standard normal and then use the standard normal table to find probabilities.
The Tables can be organised in slightly differently ways so it is important that you are aware of the format of the particular set of tables you are looking at. In the State Examination Commission’s “formulae and tables booklet, the table on page 36 gives the values for all of the shaded area under the curve from the extreme left to the particular Z value you are looking for. Other publications can give the value from the mean or 0 line to the z value, while yet others can give values for the area under the curve between minus z and plus z. The reasoning is the same in all cases but just be aware of which you are using.
For a fuller explanation see std_normal_tables.