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Nitrogen, has 5 electrons in its outer shell, Boron has only 3.

When Nitrogen Bonds with 3 Chlorine atoms, to become NCl3, it still has 2 electrons left in its outer shell, which form a lone pair. As these could bond to a single proton, (i.e. hydrogen without its electron) they have to be shown in the diagram.

NCl3 therefore has 3 bonds and 1 lone pair, so 4 things to show in the bond diagram. Making it trigonal pyramidal.

However, Boron only has 3 electrons to bond. As these are all used up in the bonds with chlorine, there are only 3 bonding pairs to show in the diagram. Therefore it is trigonal planar.

NCl3 has bond angles of 107 degrees

whereas

BCl3 has bond angles of 120 degrees.

Hope this helps.

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