Consider an example in Ruby:
puts "Matched!" unless /\d{3}-\d{4}/.match("555-1234").nil?
puts "Didn't match!" if /\d{3}-\d{4}/.match("Not phone number").nil?
The "/\d{3}-\d{4}/" is the regular expression, and as you can see it is a VERY concise way of finding a match in a string.
Furthermore, using groups you can extract information, as such:
match = /([^@]*)@(.*)/.match("[email protected]")
name = match[1]
domain = match[2]
Here, the parenthesis in the regular expression mark a capturing group, so you can see exactly WHAT the data is that you matched, so you can do further processing.
This is just the tip of the iceberg... there are many many different things you can do in a regular expression that makes processing text REALLY easy.