Carbons in organic structures come in various ways - remember it is the most versatile in its myriad of bonding. There is a system in organic that we use that helps us determine the type of carbon we are referring to. In general, this system is only for a carbon with four single bonds. It is what is on the end of those bonds that makes the carbon in the middle of a specific type. See below how we can have primary, secondary, tertiary, and quaternary carbons.
A primary carbon is only bonded to one other carbon (shown as "R" which is a typical alkyl group in organic) and the other 3 positions are hydrogens. What this really means is that the carbon is the carbon of a methyl group –CH3 in order to be a primary carbon. A secondary carbon is bonded to two other carbons and two hydrogens - we call this a methylene group –CH2–. Next, if the carbon is bonded to three other carbons and only one hydrogen, then it is a tertiary carbon. And last, if all four positions are occupied by carbons, then we have a quaternary carbon. The whole ordinal thing (1°, 2°, 3°, and 4°) is really telling us how many R-groups are on the carbon - the rest being hydrogens.
It works for H's too - Those three hydrogens on the primary carbon... you guessed it, all of those hydrogens are called primary hydrogens because they are bonded to a primary carbon. The same goes for the next one - secondary hydrogens on a secondary carbon. This is all important because we need these designations to more easily discuss and refer to specific functionalities on molecules. Sometimes only a tertiary hydrogen is involved in a reaction. It's good to know what that means.
Also notice that we even have a shorthand notation for these designations. A number with a degree sign is used so for example you can write that you have a 2°-carbon in a structure and a chemist knows that means a secondary carbon. Shortcuts and brevity are sometimes nice.
In a similar way, many functional groups and classes of compounds also take on the primary, secondary, and tertiary designations. Alcohols can be primary, secondary, or tertiary, depending on the substitutions on the carbon attached to the hydroxyl group. Once again, the number of R-groups determines the type.
Amines work the same way except now the substitutions are on the nitrogen of the amine group.
When we fully show the pathway of a reaction we call it the mechanism. A reaction mechanism shows a step-by-step process that fully illustrates the sequence of events that starts with reactants and ends with products. Sometimes it is a simple one-step mechanism while other times it is several steps to reach completion. One very common aspect to all mechanisms is to show where the electrons go - afterall, it is the redistribution of electrons between all the atoms that leads to breaking old bonds and making new ones.
Sometimes we only want to show one electron moving in a mechanism step. When only one electron is moving to a new position we use an arrow with a barb as our director. Other times, we want to move the entire electron pair - both electrons. When both electrons move, we use a full arrowhead on the arrow. Each of these types of electron displacement/movement is shown when we illustrate a bond being broken via homolytic cleavage vs heterolytic cleavage.
Chemistry lingo : We've seen the prefixes of homo- (same) and hetero- (different) before. The suffix -lytic or even -lysis means "to breakdown or loosen" but in chemistry lingo is means "to cut and separate". You can cut chemical bonds in two different ways:
In this example we are simply breaking a single covalent bond between two R-groups (alkyl groups - carbon-carbon single bond) homolytically. The result is two radical R-groups - radical meaning an unpaired electron. Note how the arrows for the electron displacements are a single-headed arrow - a barb. Keep in mind that this is a general type of split and can occur with any covalent bond - not just with R-groups.
Here in case 2 we are splitting via a heterolytic cleavage and we get an R-group cation (the one that lost the electron pair) and an R-group anion (the one that got the electron pair). Notice the arrowhead on the electron pair movement - its a double headed arrow.