This table, containing 118 little boxes with letters and numbers, is one of the most iconic images in science. And so it should be. Those 118 (and largely only a few “popular” ones) are the basic building blocks of all the matter you see around you.
The periodic table is simply an arrangement of all the elements we know about. Each little box represents an element, and the accompanying number is its atomic number- the number of protons (positive particles) held within the nucleus of a single atom of that element.
In neutral atoms, the number of electrons is equal to the number of protons, so that the charges balance out and there is no overall charge. If the number of electrons is not equal to the number of protons, there will be a positive (if less electrons) or negative (more electrons) charge and it will be called an ion rather than an atom.
As the diagram above shows, there are 7 rows in the periodic table, called (unsurprisingly) periods. Elements in each period have the same number of electron shells- different levels where electrons can reside (think about the number of circles in a Bohr diagram). The number of protons increases as you go across each period, and hence the mass of each atom generally increases (apart from some exceptions throughout the larger elements).
Also, those two extra rows down the bottom are actually part of the 6th and 7th periods, it’s just that inserting them makes the table really, really long, so for convenience, we just drop them down below and mark where they get inserted into (the asterisks in the above diagram).
In addition to the periods, there are also groups- the columns of the table. In each of these, the atoms have one extra shell for electrons to reside in as you go progressively down the table (as each is in a different period). However, the electrons are arranged in the same way within in each shell and there are the same number of electrons in the outermost shell for each element in the group. Because most chemical reactions involve the electrons in the valence shell, the fact that there are the same number of valence electrons for all elements in a group means that elements within a group have similar chemical properties.
Other things that we can tell from the table is an element’s average mass (there can be several atoms with different masses of the same element when the number of neutrons (neutral particles) in the nucleus changes while the number of protons remains the same). Many tables also include the electron configuration, which is the way that the electrons are arranged within each shell. More detailed tables may even include information about density, ionisation energy, electronegativity or specific chemical properties.
You may have also noted the variation in colours across the table. These denote “types” of elements, for example in the above table, the noble gases are blue, the non-metals are yellow, the pink in the middle is transition metals, the amber group 2 are the alkaline earth metals and the red elements on the left are the alkali metals. These “types” are all similar in many ways to each other, often being in similar states at similar temperatures, or having similar densities or bonding types.
I know this is brief, and that there’s far more on the table than this, but hopefully this is a good introduction to this central aspect of chemistry!