What are Periodic Trends?

In short

Periodic trends are regular changes in properties, such as atomic size, ionisation enthalpy and electronegativity, as you move across a period or down a group of the periodic table.

In simple words

Across a period, the nuclear charge rises while the electrons are added to the same shell, so atoms shrink, and ionisation enthalpy and electronegativity increase. Down a group, there is a new shell at each step, so atoms grow, and ionisation enthalpy and electronegativity usually fall. Fluorine is the most electronegative element, and caesium is the most electropositive of those that are stable.

Example

In period 3, the atomic radius falls from sodium ( $186\ \text{pm}$ ) to chlorine ( $99\ \text{pm}$ ). Down group 1, it rises from lithium ( $152\ \text{pm}$ ) to caesium ( $262\ \text{pm}$ ).