A team leader role is where you have more than one other person who you work with and you are there to motivate and be responsible for them during the working day. For example: you are a team leader of a busy warehouse with 15 other labourers under your wing. You are there for them to come to with any issues or problems, for you to make decisions and to lead them and ensure that the team does the work to the best of your ability.
Usually you will be promoted to a Team Leader following a period of doing the role beforehand without the responsibility to your team. You will be promoted if you have shown interest that you are looking for progression and that you have shown you can do the job in hand.
You could apply for a team leader role within another company but you need to be able to show the previous experience you have had and show a potential employer how you could be a team leader and what the role involves etc.
You may be a hands on team leader which means that you still do the same work as before the difference being that you are accountable and have a team of people who you are responsible for and who will come to you on a daily basis for answers.
You may be a team leader who is hands off and literally leads from the side observing and watching your team and guiding them in the right direction.
Whatever type you will need to have excellent communication skills and great patience. If this is a first time Team Leader role you will also realise that you need to earn the respect of your workforce, especially if you were previously one of them!