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What determines carbocation stability?

Answer
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Hint: Carbon containing a positive charge is called a carbocation, while when it contains a negative charge it is called a carbanion. These are reactive intermediates and majority of the reactions occur by their formation. These species are highly reactive and short living.

Complete answer:
A carbocation is a reactive intermediate that is formed in various organic reactions. Through the carbocation formation, the organic compounds are able to react and form different products. Carbocations are highly reactive and unstable species that react very fast and form products. A carbon, when forms a cation with 6 electrons in its valence shell, is formed by the heterolytic cleavage of a covalent bond that leads to the formation of carbocations.
There are 3 factors that determine the stability of carbocations, which are,
1.Multiple bonds: multiple bonds means the double bonds, these involve pi bonds for their formation. Multiple bonds leads to the delocalization of the positive charge formed on the carbon by resonance which provides the carbocation extra stability.
For example, ${{H}_{2}}C=CHC{{H}_{2}}^{+}$ will be more stable than $C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}^{+}$ due to the presence of double bond.
2. Lone pairs: a lone pair when present at the adjacent atom to the carbon with positive charge gives stability to the carbocation. It becomes more stable as the charge will spread over two atoms, one on the atom with lone pair and one the positive carbon.
For example, $C{{H}_{3}}OC{{H}_{2}}^{+}$is more stable than $C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}^{+}$, due to the presence of lone pair of oxygen atom.
3. Carbon atoms: carbon atoms that are adjacent to the cationic carbon provides more stability to the carbocation. This is due to hyperconjugation. The delocalization due to hyperconjugation stabilizes the carbocation.
For example, $C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}^{+}$have more stability than $C{{H}_{3}}^{+}$.
Hence, multiplicity in bonds, adjacent lone pairs, and adjacent carbon atoms affect the stability of carbocations.

Note:
As the number of carbon atoms affects stability of carbocation, the order of stability of carbocation becomes, $3{}^\circ >2{}^\circ >1{}^\circ >0{}^\circ $ these are the degree of carbons. For a carbanion the order is opposite as that of the carbocation. This is because carbanions consist of a negative charge.