When you create an index, the database creates a scaled-down copy of the data that you created the index on, and uses it to search for records in the original table.
For example, if you have a table that has 34 columns, and you create an index on just two of those columns, the index is much smaller than the original table. This means that if you run a query where only those two columns are used in the WHERE clause, the database can use the small (and therefore FAST) index to find the records in the real table.
What's more, the indexes created for searching purposes and thus they are usually faster than the real table by design.
Point is: if you don't use indexes, the database will be forced to do a 'sequencial scan' for every query. That means it must read all the data in your database to find the data you need for every query.
Think of the index as the index of a book; if you are looking for a particular chapter, you look it up in the index, the table of contents.
If that list is missing, you are forced to look at every page of the book to see if it is the chapter you want. Which is faster?