S means substitution, in which an atom/group on a substrate (the molecule which will exchange atoms) is substituted for another atom/group. E means elimination; in which a substrate loses a hydrogen and another atom/group on adjacent carbons, leaving an olefin (double bond between the adjacent carbons). N means nucleophilic, where an electron rich ion/ionic group, called the nucleophile, approches the substrate, in order to do the substitution/elimination reactions. Substitution and elimination reactions sometimes compete, and occur at the same time when we don't want them to. Solvolysis is any reaction in which the solvent of a reaction is also a reagent. Sn2 reactions can be solvolysis reaction, depending on the solvent of course. Hydrolysis (reaction with water as a solvent) is a special type of solvolysis. The nucleophiles for elimination reactions are usually strong bases, while the nucleophiles for substitution reactions ususally are not.
Experimentally, we tell the difference between Sn1 and Sn2 by following the kinetics of the reaction. If the reaction rate only depends on the concentration of the substrate, then it is Sn1. If the reaction rate depends on both the concentration of the substrate and the concentration of the nucleophile, it is Sn2. The same is true for E1 and E2. Also, for asymmetric substrates in which the chairal center is the carbon being substitued, Sn1 reactions cause racemization (loss of opitical activity), while Sn2 reactions remain optically active, but with reverse chirality. The reason for this is that in both the Sn1 and E1 reactions, the rate controlling step is the formation of a carbocation by the spontaneous dissociation of an anionic species from the substrate. For this reason, E1 and Sn1 reactions predominate for teriary substrates, which form more stable carbcations. In Sn2 and E2 reactions, the elimination/substitution reaction takes place in one step when the nucleophile approches the substrate molecule; no carbocation is generated. Therefore Sn2 and E2 reactions are done on primary substrates. Secondary substrates can go either way.
Sn2: CH3CH2CH2CH2I + Cl- → CH3CH2CH2CH2Cl + I-
E2: CH3CH2CH2CH2I + OH- → CH3CH2CH=CH2 + I- + H2O
Sn1: (CH3)3I + Cl- → (CH3)3CI + I-
E1: (CH3)3I + OH- → (CH3)2C=CH2 + I- + H2O