A company car is a car made available by the employer for the private use of an employee. Private use includes ordinary 'home to work and back commuting journeys.
You have to pay tax on any benefit in kind you receive, such as a company car. Until April 2016, people earning less than £8,500 a year did not have to pay tax on benefits in kind, but this threshold exemption for low earners has been abolished. For more information, see the website of the Low Incomes Tax Reform Group.
Employees have to pay tax on the 'car benefit', depending largely on individual earnings and on the car’s carbon dioxide and nitrogen oxide emissions. From April 2018, diesel cars incur a higher tax charge than petrol cars. There is HMRC guidance available on this.
A further separate charge is made if the employee is provided with fuel for private use.
GOV.UK's Tax on company benefits webpage includes useful information on company cars.