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A sigma (σ) bond is formed by direct orbital overlap along the internuclear axis and allows free rotation. A pi (π) bond is formed by lateral overlap of p orbitals above and below the internuclear axis and restricts rotation. Double bonds consist of one σ and one π bond; triple bonds have one σ and two π bonds.
You already know from covalent bonding that atoms share electrons by overlapping their orbitals. The next step is recognizing that not all overlaps are equal — the geometry of how orbitals meet determines the bond's properties. A sigma (σ) bond forms when two orbitals overlap head-on, directly along the line connecting the two nuclei. Think of two people shaking hands — the contact point is right between them on a straight line. This head-on overlap produces a cylindrically symmetric electron cloud wrapped around the internuclear axis. Because that cloud is symmetric all the way around, one atom can rotate relative to the other without breaking the bond. Every single bond you have drawn so far is a sigma bond.
A pi (π) bond forms in a fundamentally different way. Instead of overlapping head-on, two p orbitals sit parallel to each other and overlap sideways — above and below the internuclear axis. Imagine holding two magnets side by side so their fields merge in the space between them, but not along the line connecting their centers. The resulting electron density exists in two lobes, one above and one below the bond axis, with a node (a plane of zero electron density) right along the axis itself. This geometry means that rotation around the bond would break the lateral overlap and destroy the pi bond, which is why double bonds are rigid and do not rotate freely.
When you see a double bond (like C=C in ethylene), it is not simply "two of the same bond." It is one sigma bond providing the structural backbone plus one pi bond layered on top, locking the molecule into a planar geometry. A triple bond (like C≡C in acetylene) takes this further: one sigma bond plus two pi bonds, with the two pi bonds oriented perpendicular to each other. The sigma bond is always stronger than an individual pi bond because head-on overlap is more effective than sideways overlap, but the combination of sigma plus pi makes double and triple bonds progressively shorter and stronger overall.
Understanding sigma and pi bonds is the key to predicting molecular geometry and reactivity. The rigidity of pi bonds explains why cis and trans isomers exist around double bonds — rotation cannot interconvert them without breaking the pi bond. It also explains why pi bonds are more reactive than sigma bonds: the electron density in a pi bond sits exposed above and below the molecular plane, making it accessible to electrophilic attack. This concept becomes central when you move into hybridization theory and the chemistry of alkenes and alkynes.