1-to-1 (or One-to-One) lessons are those with just 1 student and 1 teacher.
Often, although not always, they are private lessons.
As with other lessons, these need to be thought out well and because the student will only be able to interact with the teacher (instead of with other members of the class) you will need to have plenty of extra activities prepared in case the student completes those you have set in a shorter time than you envisaged.
Useful Links
Private English Lessons – a look at teaching outside the classroom environment
Private English Lessons to Businesses – to businesses
A First Private TEFL Lesson – how to get through that first one-to-one lesson when you don’t really know who or what you’ll be teaching