The Dimensional Anchor is a block that loads chunks. There is a limit on the number of chunks each non-operator player can load in a SMP world, and each anchor can load chunks in an adjustable area of 1x1, 3x3, 5x5, 7x7 or 9x9.
Note: In Singleplayer, it's impossible to use Dimensional Anchors or other chunk-loaders to load other dimensions such as the Nether or The End. This is a problem with the world and not with Tekkit.
Right clicking the Dimensional Anchor opens this GUI. If you are in singleplayer, OP, or the owner of the chunkloader, you can change the size of the loaded area without breaking and replacing it (which would make you the owner).
The green button expands the area loaded by this chunkloader by one chunk, and the red button shrinks it, by one chunk.
As you can see, there is a limit on the number of chunks that each player may force to be loaded. In singleplayer, or if the owner of the chunkloader is an op, there is no limit.
In multiplayer, if you're op, you can change it to the owner (that being you) or you can change it to the server. If you change it to the server, it will always load the chunk (even when you're away).