Whereas electrophiles have areas of electron deficiency, nucleophiles have areas that are electron rich.  A nucleophilic "nucleus-loving" species will tend to attack electron-deficient areas.e.g.:

It must be stressed that there only needs to be a small imbalance in charge to favour a reaction along one path.  However, a large charge imbalance is certainly not an impediment to the reaction. In some cases, the charge imbalance itself is caused by the approach of the reagents themselves, e.g. bromine and ethene:

When the bromine molecule is far enough away, it is not polarised (clearly as both atoms are identical), however, on approaching the electron dense area of the pi bond of ethene, the bromine molecule becomes polarised; the electrons in the bromine-bromine bond are repelled by the pi electrons of the alkene, so the nearer of the two atoms becomes slightly positively charged, and the farther consequently becomes slightly negatively charged.  This is enough of an imbalance to allow the electrons in the pi-bond to attack bromine in this familiar addition reaction.

The concept of electrophiles and nucleophiles may remind you of acids and bases, which is not surprising, as there are many similarities.

The Brønsted definition of an acid is a proton donator, and that of a base is a proton acceptor, and the Lewis definition generalised this to include acids as electron pair acceptors, and bases as electron pair donors.  This definition therefore includes some species not previously thought of as acids and bases e.g. boron trifluoride:

The Lewis definition of acids and bases is quite similar to electrophiles and nucleophiles, the former being essentially electron acceptors, and the latter being electron donors.  Electrophiles and nucleophiles also bear a relationship to oxidizing and reducing agents. Oxidizing agents can be viewed as electron donors, and reducing agents can be viewed as electron acceptors.

The table above may prove useful as a reference guide to various common electrophiles and nucleophiles.