What does it mean to mix an s and p orbital?

As you can see on the diagram, s and p orbitals are at different energy levels.
However, the s and p orbitals can move to a energy level in between both of them. This is known as hybridisation.
s, sp1, sp2 and sp3 orbitals can only overlap end-on-end to form σ bonds whereas p orbitals can overlap sideways to form \( \pi \) bonds.
The first bond must always be a σ bond but the second and third bond must be a \( \pi \) bond.

Single bonds

When p orbitals are involved in forming single bonds, they are modified to include some s orbital character. The orbital is slightly altered in shape to make one of the lobes of the p orbital bigger.
When one s orbital and three p orbitals are hybridised, the hybrids are called sp3 hybrids. Each orbital has 1/4 s character and 3/4 p character.
All the bonds in ethane are σ bonds.

A C=C double bond, as found in alkenes such as ethene, is made up of a σ bond and a pi (\(\pi\)) bond.
The carbon atoms involved in the double bond will each form three σ bonds. This is an example of sp2 hybridisation.
This leaves each carbon atom with one spare outer electron in a 2p orbital. When these two p orbitals overlap they form a \( \pi \) bond.

In the nitrogen molecule, N≡N, hydrogen cyanide, H-C≡N and ethyne, H-C≡C-H, there are triple bonds.
The triple bond is formed from two \( \pi \) bonds and one σ bond. The two \( \pi \) bonds are at right angles to each other.
This is an example of sp hybridisation. The N and C atoms in HCN are both sp hybridised