Every member of an F1 team is important, but perhaps the two most important people are those that drive the car around the track. These are usually the most well-known members of the team, and they are also usually the ones that get paid the most.
They will be in contact with their race engineers throughout the race, getting instructions and advice, and general communication. The race engineer is usually someone that they have a strong bond with, as they are their link to the rest of the team and the data from the car during the race. The race engineer sits alongside other engineers, usually data analysts.
These are the people that take all of the data from the car, amongst other data, and relay it back to the race engineer who can then pass it on to the driver. They monitor every aspect of the car, from temperatures to tire wear to more serious damage as well. Then come the mechanics, and these are the people who get to work on the car when it pulls in for a pit stop.
Most pit stops involve a tire change, and it takes three mechanics per tire. There needs to be one person operating the wheel gun, and then one to take the old tire off and someone to put the new tire on. Alongside the 12 tire men, there will be someone to stop and release the car, and various others to help with any repairs or to make sure everything goes according to plan.
There will be a team of mechanics for each driver, and there will be extra people on hand in case the car needs a more serious repair, such as a change of front wing. Aside from the mechanics and engineers, there is of course the team principal. This is the person who is at the head of the team, and they guide their staff towards (hopefully) glory each season.
They are often the face of the team, alongside the drivers, and the person that may receive the most scrutiny from the media. They do a lot of press conferences, and usually must answer for the team when things go wrong and take some of the praise when things go well. They may also be the owners of the team, but often the teams are owned by other people.