Electrophilic addition reactions are transformations in which reagents are added to compounds containing multiple (double or triple) bonds.  The mechanism goes via carbocation intermediates, the formation of which is dictated again by relative stability (compare with the SN1 reaction).  The carbocations formed in this type of reaction are trapped by nucleophiles, exactly as in the SN1 reaction, with resultant formation of the addition product(s).  The following series of graphics may help you visualize the events occurring during this reaction.

Unsaturated substrate (alkene or alkyne) and electrophilic species (e.g. H+) come into close proximity.

Pi electrons from substrate are donated towards the electrophile, bond formed between one of the carbon atoms in the double bond and the electrophile.

Donation of electrons to electrophile results in carbocation formation.  Same stability rules apply as elsewhere (3^o>2^o>1^o).

Nucleophilic species approaches and donates electron pair towards cation resulting in C-Nu bond formation.

Overall, the reaction results in addition of an electrophile and nucleophile to the multiple bond.

The following animation puts these events is sequence:

When unsymmetrical substrates are employed, Markovnikoff addition occurs.  Essentially, the major product of addition will be the one that results from the most stable cation intermediate.  The following is an example:

Peter Norris, Ph.D. 1998