Be warned that the SD card reader has a small switch that gets is either open or closed based on the position of that tab (much like old cassette and VHS... that tab does not actually do anything other than push a button in the reader)
There is also a method to write protect that card through software... but is very very rarely ever done (Difficult on many machines as it requires a special bit to be set on the SD card which many OSes dont support writing to)
If the card cannot be written to on your computer, try toggling the position of the plastic lock tab, then try a new machine, or new card.
If this is the only card that affected on your computer or if this card does not work on another machine either, it may be defective.
If multiple cards do this to you, you have a busted card reader

(or a busted switch in the card reader)
Careful with no-name or knock-off memory cards as well... There have been many incidents where the actual memory in a card is far less than advertised, and some electronic trickery can make your computer 'think' that all the space is there. When you start to fill up the card some interesting things will happen
Edit:
Hackaday link for a hardware SD Card locker (via setting a bit on the card)
http://hackaday.com/2014/01/18/the-tiniest-sd-card-locker/
Sparkfun link to SD Card socket...
https://www.sparkfun.com/datasheets/Prototyping/SD-Socket-PP-19607.pdf