According to the Lewis definition, Lewis acids are substances that accept electron pairs - electron acceptors, while Lewis bases are substance that donate electons - electron donors.
A classic example of a Lewis acid-base reaction takes place between ammonia (#NH_3#) and boron trifluoride (#BF_3#).
Since boron (#B#) is in group 13, it only has 3 valence electrons, which means it can only form three bonds. #B# bonds with three #F# atoms and adds 3 more electrons to its outermost shell, for a total of 6 electrons (3 it owns and 3 come from the covalent bonds it has with #F#).
Notice that it still needs 2 more electrons to complete its octet, i.e. to have 8 electrons in its outermost shell, therefore can accept a pair of electrons. This is where #NH_3# comes into play.
#N# is in group 15, which means it has 5 valence electrons and can form three bonds (this is because out of the five valence electrons, only 3 are unpaired) - it can therefore donate a pair of electrons.
Here's what happens during their reaction. Since it is bonded to three other atoms, #B# is #sp^2# hybridized. This means that one of its three 2p-orbitals (#2p_z#) is empty. The lone pair of electrons on #N# is picked up by #B#'s empty p-orbital and a covalent bond is formed between the two molecules.
#NH_3# acted a Lewis base - it donated a pair of electrons, while #BF_3# acted as a Lewis acid - it accepted a pair of electrons.
