This is the variation of the properties of elements in a regular pattern across the period and down the group. Some periodic trends include: melting and boiling points, ionization energy, thermal conductivity, etc.

This can be defined as the measure of the tendency of an atom to attract and form bonds with electrons. Non-metals tend to attract electrons more readily than metals because they require less energy to gain electrons than to loose electrons. The nature of electronegativity is effectively described thus: the more inclined an atom is to gain electrons, the more likely that atom will pull electrons toward itself.
From left (metals) to right (nonmetals) across the period, electronegativity increases. This is because if the electron shell of an atom is less than half full it has a greater tendency to attract rather than donate electrons.
Down the group, electronegativity decreases. This is because of increase in distance between electrons and the nucleus or a greater atomic radius. According to the Paulings scale of electronegativity, Flourine (4.0) is the most electronegative element while Cesium(0.7) is the least.

This can be defined as the amount of energy required to remove an electron from a neutral atom in its gaseous state to form an ion. Since it requires less energy for metals to loose electrons to form positive ions and more energy for non-metals to loose electrons to form positive ions(cations), Ionization energy increases across the period from left to right and decreases down the group.
Factors that affects ionization energy

• Distance of the outermost electrons to
  the nucleus

The closer the distance, the higher the ionization energy.

• Size of the positive nuclear charge

The greater the nuclear charge, the greater the ionization energy

• Screening effect of the inner electrons
Electron shielding describes the ability of an atom's inner electrons to shield its positively-charged nucleus from its valence electrons. When moving to the right of a period, the number of electrons increases and the strength of shielding increases. As a result, it is easier for valence shell electrons to ionize, and thus the ionization energy decreases down a group. Electron shielding is also known as screening.

Electron affinity of an element can be defined as its ability to accept an electron. Unlike electronegativity, electron affinity is a quantitative measurement of the energy change that occurs when an electron is added to a neutral gas atom. The more negative the electron affinity value, the higher an atom's affinity for electrons. Electron affinity increases from left to right across the period and decreases down the group due to increase in atomic radius.

Electropositivity can be defined as the tendency of an atom to donate electrons and form positively charged cations. Electropositivity decreases across the period from metals to non-metals and increases down the group.

This can be defined as the tendency of an atom to lose or donate electrons or possess metallic properties like malleability and electrical conductivity. This property decreases from left to right across the period and increases down the group.

The distance between the centre of the nucleus and the outermost shell of an atom is known as the atomic radius. In a group the atomic size increases due to the addition of shells as we move from one period to another. Across a period the atomic size decreases as the number of shells remain the same while the nuclear charge increases. This leads to the pulling of electrons from the outermost shell towards the nucleus thereby decreasing the size. This trend decreases across the period from left to right and increases down the group.