Shortcut to the citrus forum <--Click that...you should find the help you need there.

Your tree is grafted (that is, the roots are originally a different plant to the branches above). It's done to give a good quality fruiting tree a good root system (they don't always naturally occur on the same plant). What's happened is the rootstock has produced it's own branches. You need to cut those off or you could lose the graft which would give you the best fruit. This doesn't always happen, but it's not unusual.

Wow, I would never, ever have worked that one out! Thank you! Will cut them off then ☺.