Flagship
A flagship is a ship that has the command over a group of ships. The name flagship comes from the fact that the commander flew an identifying flag from this ship, showing the other ships in the group that he was on that ship, and they should look at that ship for orders.
Secondary, in the past the orders where given by using flag signals.
In the Military navy, officers of high enough rank to lead a group of ships, where known as flag-officers. Their flag was a command flag. Command flags may from some nations look like national flags, but they are not to be flown instead of the national flag, they are flown from the mast top (where they are best visible) and there are different designs depending on the rank, from a swallow tail cut out, to the addition of a number stars or balls. But also different colours and shapes are used.
In the past the biggest meanest ships was often chosen as a navy's flagship. But sometimes a commander had a personal favourite. In modern day navies design ships specifically for flagships duties, they are then equipped with more communication equipment and accommodation to house the commanding officer and staff.
Merchant companies sometimes refer to their oldest, or best looking, or best performing, or best equipped ships as their flagship. Depending on the type of company and their specific business. It is not known of any specific flag is used to identify these ships.
This is an interesting article - I like that the flagship does not necessarily have to be the biggest, though it often is.