Charing Cross is a train and London Underground station in London, and because of it the area around it is also referred to as "Charing Cross". heyoka goes into the original naming of the area and station so I won't deal with that here.
It lies nearly at the western end of The Strand - the road continues another quarter of a mile or so to Tralfagar Square. It is often considered the nominal centre of London - all road signs marked with distances to London are actually the distance to the Cross in front of the station.
NB: Charing Cross Road actually ends at Trafalgar Square, not at Charing Cross station!
The area is a busy business district, with plenty of shops, bars and restaurants, together with office blocks of all varieties. It is on the edge of the West End theatre district and actually has a small theatre (the Playhouse) kind of within the structure of the station. On the other side of the station is Northumberland Avenue, and past this is Whitehall, best known for being the home of the Offices of State. The Palace of Westminster, where the British Houses of Parliament are, is about 15 minutes walk. The area is also popular as it's right by the River Thames, directly oppposite from the London Eye.
The original station was built by John Hawkshaw in 1863, and includes a hotel now owned by The Thistle group. More interesting is that the station arch is no longer a station arch - instead it houses the huge Embankment Place office, the main UK headquarters of PricewaterhouseCoopers. This interesting building (which you get a great view of from the London Eye) is 9 stories tall ABOVE the station, with an entrance below the station. The office sits on pillars which go through the station, and on entering below the station, the lifts take you up in enclosed lift shafts between platforms 5 and 6 into the office.
The mainline railway station has links down to the south-east of London and Kent. However, it's not the busiest of stations. All trains from Charing Cross stop at Waterloo East just across the river (and an interchange with the huge Waterloo station with trains to the South West) and Eurostar services to France and Belgium, and then most trains stop at London Bridge station. This has its own terminus platforms as well, and is arguably a more significant station.
On the Underground side, there is an interesting history.
Originally, Charing Cross underground station was down right by the river - what's now called Embankment station. This is served by the Northern line (Charing Cross branch) and Circle & District lines. Separately, there was then a Trafalgar Square station, about 5 minutes walk away, at Trafalgar Square.
In 1977 to commemorate Queen Elizabeth's 25 years on the throne, the Stanmore branch of the Bakerloo line (which went from Baker Street to Stanmore) was extended down to Bond Street, Green Park and into Charing Cross, and renamed the Jubilee line. This was built under Charing Cross station and called Charing Cross. The Bakerloo line platforms at Trafalgar Square were brought into this station, with underground foot tunnels put in place between the Jubilee and Bakerloo line platforms. The former Charing Cross station was renamed Embankment. A Northern line station was also opened at Charing Cross, although in fact it is only about one minute's walk from Charing Cross to Embankment. There were plans to extend the Jubilee line along The Strand and Fleet Street into the city, but these never happened.
More recently, in preparation for the Millennium Dome, the Jubilee line was rerouted again. The link into Charing Cross was closed off after Green Park, and the line extended to Westminster, Waterloo, London Bridge, Canary Wharf, Greenwich (for the dome) and onto Stratford in the East End.