Essentially numerology is treating numbers as divine and using them to predict future events or to understand the will of a deity. The idea goes back at least to Pythagoreans, who believed that numbers and their relationship with reality would reveal the secrets of the universe. In more modern times it refers to using arbitrary connections between letters and numbers, looking for patterns that arise out of various mathematical processes and assuming that these can tell you something about the world.
Often it will mean taking a word or name, giving letters a numerical value: A=1, B=2 etc, then doing an arbitary calculation on those numbers to somehow come to a conclusion. Sometimes it uses your date of birth or a given number like a NI or Social Security No. and performing arithmetical contortions on it. Numerologists can then provide you with a "reading" similar to those provided by astrologers, handwriting analysts or palm readers. With about as much accuracy.
The idea of a 'Lucky Number' is numerology, as are things like looking for patterns in convoluted extractions from holy books such as espoused in The Bible Code by Michael Drosnin. He used a method found in a much criticized study by a group of Israeli mathematicians who had applied an Equidistant Letter Sequence method to the Hebrew Bible (writing out every 7th or 5th or whatever letter and wrapping the resulting text string around a cylinder, flattening it and using the resulting table of text to go pattern-hunting in word or number strings) and found what they called statistically significant correlations between dates and names. Drosnin applied it to an English version to make predictions about the future and the power of 'God's secret code'. he has written several books and spawned a whole industry of conspiracy mongers looking for and finding after-the-fact "proof" that Trump would be president or 9/11 would happen. Numerology is also a topic taught in Arithmancy class in Harry Potter and was described as the practice of assigning numerical value to words in order to predict the future.