Nomenclature:
Functional group suffix = -ene (review)
Simple 1,2-alkenes can be described as cis- or trans- (review)
More complex alkenes are best described as E- or Z- based on the Cahn-Ingold-Prelog priority rules (review)

Stability:
There are 3 factors that influence alkene stability:
1. Degree of substitution: more highly alkylated alkenes are more stable, so tetra > tri > di > mono-substituted.
2. Stereochemistry: trans > cis due to reduced steric interactions when R groups are on opposite sides of the double bond.
3. Conjugated alkenes are more stable than isolated alkenes.
 

Structure:
 

The alkene functional group consists of two sp2 hybridized C atoms bonded to each other via a s and a p bond. The p bond is produced by the side-to-side overlap of the p-orbitals not utilized in the hybrids (see left). The substituents are attached to the C=C unit via s bonds. The 2 C of the C=C and the 4 atoms attached directly to the C=C are all in the same plane.

Reactivity:

A  p bond  is a region of high electron density (red) so alkenes are typically nucleophiles. Alkenes typically undergo addition reactions in which the p bond  is converted to two new s bonds.