Starting with an alkene, adding strong acid gets us to a carbocation (A–>B). If the counterion to that acid is a decent nucleophile (think Cl-, Br-, or I-) then it will then add to it, giving us the addition product D. Alternatively if we use an acid like H2SO4 (which has a poorly nucleophilic counterion) in the presence of water or another nucleophilic solvent, we can also get addition products. The pathway A –> C –> D is an example of alkene addition.
Alternatively the carbocation can be generated through loss of a leaving group (B–> C) . Attack of that carbocation by a nucleophile (e.g. a nucleophilic solvent, again, like H2O or CH3OH) will give us a new product. The pathway B –> C –> D is what we call the SN1 reaction.
Finally, if the carbocation is generated through loss of a leaving group but there isn’t any reasonably good nucleophile present, elimination may occur to give the alkene. The pathway B –> C –> A is what we call the E1 reaction.
So there you have three very important reactions all intersecting through a common intermediate.
[Remember that leaving groups (LG) are just nucleophiles (Nu) acting in reverse. That’s why there aren’t double [equilibrium] arrows going between B, C and D]
One complication that’s left out here is carbocation rearrangements. Important to remember that they can occur but I couldn’t think of a way to put them in while keeping the diagram neat and tidy. :- )