A felting needle has small barbs in the end that, when stabbed through wool, catch on the scales of the fibre and push them together. The more and more you stab, the more fibres matt together slowly turning the wool into solid felt. Different needles come with varying numbers of barbs. The more barbs, the quicker the felting but less barbs will give you more accuracy with fine detail work.
Triangluar needle, barbs on three sides, is a sturdy needle good for working with course fibres and firmly attaching pieces. Not great for detail or a neat surface. A sturdy needle good for working with course fibres and firmly attaching pieces.
Spiral needle, barbs that twist around the end, makes them felt quickly and gives a neat finish minimising the surface holes you can get with other needles. Good for detail felting on dense projects. Not a good solution for doing bulk sculpting work.
Reverse needle, barbs on these needle go the other way, pulling the fibres out rather than pushing them in. This is useful to create a fluffy finish on a well felted piece.