To elucidate a simplistic example of this, if you had a company table and an employee table and each company row could have many employee row associated with it, you would (assuming they were correctly designed) have two relational tables and one relationship.
Normalization is the process by which a series of rules known as the normal forms are applied in sequence to a tabular data set that has not been correctly designed in accordance with relational principles. As each rule is applied, the data set achieves higher degrees of normalization. Generally, these rules dictate that redundant information should be moved into new relations (tables). No information is lost in this process, however the number of tables generally increases as the rules are applied. Thus to reconstruct information that once was in one table, a relational query must pull data from more than one table in a join operation.
Fully normalizing your data will ironically not make all data operations more efficient in your average “relational” database. Oracle Press books at one time made the bold statement that that no major application can be programmed in Third Normal Form! This does not reflect any particular problem with the relational model per se, rather it is an artiface of the current state of the art and computing power. Highly relational designs generally reduce the redundancy in the system at a cost of computing power. Despite the many innovations and efficiencies of modern database systems, it still takes longer to bring together information from diverse sources (i.e. related tables) than it does to get all the information you need from a single source, i.e. one big table. Often the most practical structure for reporting on large stores of information is selectively denormalized. However the most practical structure for ensuring data integrity in a transactional system is almost highly normalized. This no short coming of the relational model itself, rather it is an observation of how the model has been implemented in popular commercial databases.