The simplest way is to make all readers wait until the writer is done, which is known as a read-write lock. Locks are known to create contention especially between long read transactions and update transactions. MVCC aims at solving the problem by keeping multiple copies of each data item. In this way, each user connected to the database sees a snapshot of the database at a particular instant in time. Any changes made by a writer will not be seen by other users of the database until the changes have been completed (or, in database terms: until the transaction has been committed.)
When an MVCC database needs to update a piece of data, it will not overwrite the original data item with new data, but instead creates a newer version of the data item. Thus there are multiple versions stored. The version that each transaction sees depends on the isolation level implemented. The most common isolation level implemented with MVCC is snapshot isolation. With snapshot isolation, a transaction observes a state of the data as when the transaction started.
