The Lunar Nodes are the points at which the Moon's orbit crosses the ecliptic. There is a North Node and a South Node: these are the points where the Moon crosses this plane going north and south respectively. However, since the two nodes are 180º apart, any aspect (apart from the conjunction) which has an effect on one will have a similar effect on the other. When the horoscopes in UK Online refer to The Lunar Node, this means that either node is aspected.
Traditionally, the Lunar Nodes have been referred to as the Dragon's Head and Tail. This is because, when the Sun is near them, the New and Full Moons are eclipses. The mythological idea was that the nodes were dragons which ate the Moon or Sun.
The astrological significance of the Lunar Nodes has been disputed. Some astrologers believe that the North Node has a positive effect, possibly similar to that of Jupiter. The South Node traditionally was given a more negative rôle, similar to that of Saturn.
More recently, astrologers have found a meaning similar to that of the Moon. This makes sense, since the Nodes represent a meeting of Lunar and Solar energies (similar, perhaps, to a Sun/Moon Midpoint). Indeed, both Nodes probably have a connection with meeting people; and, in particular, with meetings which involve feeling (because of the connection to the Moon). Many people still see a positive/negative influence from the North and South Node: the North Node is taken to mean "coming together" with other people, while the South Node means "separating". However, it is clear that much more work needs to be done in this area.
The exact positions of the Nodes can be calculated in one of two ways. Traditionally, astrologers used the mean Lunar Nodes, which moved along the zodiac at a constant rate (one complete circle every 18.6 years). More advanced calculations have produced ephemerides for the "True Node", which includes the effect of the Moon's wobble. The horoscopes in UK Online use the True Node, although, again, much more work needs to be done before we can be sure which measure is more accurate.