At a simple level, you will have drawn ethene showing two bonds between the carbon atoms. Each line in this diagram represents one pair of shared electrons. Ethene is actually much more interesting than this.
Ethene is built from hydrogen atoms (1s1) and carbon atoms (1s22s22px12py1). The carbon atom doesn't have enough unpaired electrons to form the required number of bonds, so it needs to promote one of the 2s2 pair into the empty 2pz orbital. This is exactly the same as happens whenever carbon forms bonds - whatever else it ends up joined to.
Promotion of an electron
There is only a small energy gap between the 2s and 2p orbitals, and an electron is promoted from the 2s to the empty 2p to give 4 unpaired electrons. The extra energy released when these electrons are used for bonding more than compensates for the initial input. The carbon atom is now said to be in an excited state.
In the case of ethene, there is a difference from, say, methane or ethane, because each carbon is only joining to three other atoms rather than four. When the carbon atoms hybridize their outer orbitals before forming bonds, this time they only hybridize three of the orbitals rather than all four. They use the 2s electron and two of the 2p electrons, but leave the other 2p electron unchanged.
The new orbitals formed are called sp2 hybrids, because they are made by an s orbital and two p orbitals reorganizing themselves. sp2 orbitals look rather like sp3 orbitals that you have already come across in the bonding in methane, except that they are shorter and fatter. The three sp2 hybrid orbitals arrange themselves as far apart as possible - which is at 120° to each other in a plane. The remaining p orbital is at right angles to them.
The two carbon atoms and four hydrogen atoms would look like this before they joined together:
The various atomic orbitals which are pointing towards each other now merge to give molecular orbitals, each containing a bonding pair of electrons. These are sigma bonds - just like those formed by end-to-end overlap of atomic orbitals in, say, ethane.
The p orbitals on each carbon are not pointing towards each other, and so we'll leave those for a moment. In the diagram, the black dots represent the nuclei of the atoms. Notice that the p orbitals are so close that they are overlapping sideways.
This sideways overlap also creates a molecular orbital, but of a different kind. In this one the electrons aren't held on the line between the two nuclei, but above and below the plane of the molecule. A bond formed in this way is called a \(\pi\) bond.
For clarity, the sigma bonds are shown using lines - each line representing one pair of shared electrons. The various sorts of line show the directions the bonds point in. An ordinary line represents a bond in the plane of the screen (or the paper if you've printed it), a broken line is a bond going back away from you, and a wedge shows a bond coming out towards you.
Be clear about what a \(\pi\) bond is. It is a region of space in which you can find the two electrons which make up the bond. Those two electrons can live anywhere within that space. It would be quite misleading to think of one living in the top and the other in the bottom. The \(\pi\) bond dominates the chemistry of ethene. It is very vulnerable to attack - a very negative region of space above and below the plane of the molecule. It is also somewhat distant from the control of the nuclei and so is a weaker bond than the sigma bond joining the two carbons. All double bonds (whatever atoms they might be joining) will consist of a sigma bond and a pi bond.
The shape of Ethene
The shape of ethene is controlled by the arrangement of the sp2 orbitals. Notice two things about them:
They all lie in the same plane, with the other p orbital at right angles to it. When the bonds are made, all of the sigma bonds in the molecule must also lie in the same plane. Any twist in the molecule would mean that the p orbitals wouldn't be parallel and touching any more, and you would be breaking the \(\pi\) bond.
There is no free rotation about a carbon-carbon double bond. Ethene is a planar molecule.
The sp2 orbitals are at 120° to each other. When the molecule is constructed, the bond angles will also be 120°. That is approximate though; there will be a slight distortion because you are joining 2 hydrogens and a carbon atom to each carbon, rather than 3 identical groups.
Jim Clark (Chemguide.co.uk)